Currently with the Belgian national side at this summer's Euros in France, the 22-year-old was given special permission from national team manager Marc Wilmots to travel to the nearby French city of Bordeaux in order to undergo his medical.
According to the Daily Mail, the energetic forward is set to arrive at the club in a deal worth£33.2million, signing a five-year contract with the Premier League side.
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The prolific striker is, however, not the first player to join the Blues from Ligue 1. In fact, Chelsea have a history of immensely talented players arriving from the French league.
As Blues fans will remember, some of the best players during the Roman Abramovich era have been recruits from the nation across the English channel.
Here's a look at five of the most influential players from Ligue 1 to have graced the Bridge under the Russian billionaire's ownership.
Arguably the best foreign player to have played for Chelsea.
Ivorian striker Didier Drogba is now a household name, not only among Blues fans, but Premier League supporters as well.
The Stamford Bridge legend arrived from Marseille in the summer of 2004 for a club record transfer fee of £24 million, having led the French giants to the UEFA Cup final the previous season.
Considered an emerging talent at the time, the former Champions League winner was one of Jose Mourinho's first, and perhaps best, signings as Chelsea manager.
Drogba's contributions for the Blues are unparalleled, having scored a 100 goals in 226 appearances for the club.
Scoring in three League Cup finals, four FA Cup finals, as well as the equaliser and winning penalty in the 2012 Champions League final against Bayern Munich, has earned the striker a reputation of being a serial match winner.
The former Chelsea Player of the Year's influence on the team extends beyond the pitch, as the Ivorian provided an immense presence in the dressing room as well.
Drogba's mere presence in the side raised the morale and performance of the rest of the team, as evident from Chelsea's title winning season in 2015, where the legendary striker was sparingly used but was always there in case the team needed him.
The iconic striker's immense strength, as well as exquisite hold up play against opposition defenders, made him one of the best forwards with his back towards goal, with the ability to create a chance out of nothing.
Hence, Chelsea fans can be optimistic about the fact that Batshuayi will arrive from the same club as the former African Player of the Year, and being just 22-years-old, the Belgian has ample amount of time in which to emulate the Stamford Bridge legend.
Having arrived from Lille in 2012, Eden Hazard has seen a sharp rise to stardom at the Bridge, winning the Chelsea Player of the Year award in 2014 and 2015, in addition to bagging the PFA Player of the Year trophy during Chelsea's title winning season little over a year ago.
Never have the Chelsea faithful witnessed a talent of such tremendous ability at the club. The Belgian offers genuine skill and spark to the team's attack, reminiscent of another Chelsea legend, Gianfranco Zola.
Therefore, the winger is the crown jewel of the current Chelsea side, as well as the Belgian national team.
During a dismal 2015/2016 campaign with the Blues, Hazard was considered one of the main culprits in the club's poor performances, as the Belgian captain proved to be largely inconsistent during the season, primarily due to niggling injuries and the burden of excessive defensive responsibilities.
However, during the last few games of the season, Hazard showed what he is truly capable of, after fully recovering from a hip injury.
In the title deciding game against London rivals Tottenham Hotspur, the midfielder scored a stunning equaliser late on, handing the title to Leicester City as a result.
Hazard's confidence and form seemed to be slowly but surely returning, as the winger scored another stunning solo goal at Anfield, weaving past a horde of Liverpool players.
The 25-year-old's return to form came at the ideal time for Belgium. Barring the opening game loss to the Italians, Hazard has been a constant threat during the European Championships, putting on a masterclass performance in a 4-0 round of 16 win against Hungary, a game in which the skipper was simply unstoppable.
In the same game, Hazard provided an assist for Batshuayi and Chelsea fans will be relishing the prospect of the two combining next season.
Before being crippled by constant injury problems, Michael Essien was a massively influential figure in Chelsea's midfield.
The Ghanaian possessed endless stamina and endurance, and was a constant menace for opposition attackers and midfielders.
Playing alongside the likes of Frank Lampard, Claude Makelele, and Michael Ballack, Chelsea boasted one of the strongest midfield lineups at one point in the presence of the former Lyon man.
The former African Player of the Year was an instrumental figure during the club's most successful period between 2005 and 2012, combining immense strength with great mobility and movement.
It was a common occurrence for Essien to cover more than 10km during the course of a game, essentially following the ball wherever it went. A presence of that kind has been greatly lacking in the side and is yet to be truly restored.
After the legendary Makelele, Essien was arguably the most underrated player in the Chelsea team, as is the case with a lot of box-to-box midfielders.
Essien's presence was not always apparent during the game, as his role in the team restricted him to mostly the dirty work in midfield, as opposed to the exciting and sparkling aspects of the game. His absence, however, from the team was often apparent and strongly felt, especially by teammates.
Despite being frustrated by injuries during the latter half of his stay in London, his contributions to the club will always be remembered by Blues fans.
Hailed as one of the best keepers in Premier League history, the Czech Republic international joined the Blues from French club Rennes during the same time as Drogba.
The 34-year-old keeper clinched the Golden Glove award last season with Arsenal, but most of his appearances in the league were with Chelsea.
Cech holds the record for the highest number of clean sheets in a season (21) and the all-time highest clean sheets in the Premier League (174), with the former occurring during 2004/2005 with the Blues.
Having drawn comparisons to Italian legend Gianluigi Buffon, the former Chelsea keeper has a similar style and stature to the Juve keeper, possessing great positioning ability as well as height.
For eight seasons, the spine of the West London club comprised the imposing keeper, Terry, Lampard, and Drogba, a combination that brought constant success to the club.
A critical head injury to the veteran keeper in a game against Reading during the 2006/2007 season was the first major setback the keeper faced during his time at Stamford Bridge, leading many to question his ability to get back to his best.
Despite missing a large part of the campaign, the Chelsea legend came back to the team sporting a protective mask, something more recent fans associate him with.
It's hard to say how severely the injury affected the player's future performances, but he was back to his best within a year. and was a crucial part of the team's 2010 league win as well as the 2012 Champions League win.
Even at the age of 34, Cech is showing no signs of slowing down, having fully taken over the goal keeping role at the Emirates. Many have questioned Cech's move to Arsenal, but he will always remain a Blues legend.
Just like Drogba, French defender William Gallas joined the Blues from Marseille.
Currently retired from all forms of football, the versatile defender arrived at Stamford Bridge in the summer of 2001 under the management of Claudio Ranieri.
The Frenchman had the opportunity to play alongside both Terry and Marcel Desailly, the last captain at the Bridge before Terry took over the reigns.
Despite being a crucial part of Ranieri's team, it was under Mourinho that the former Arsenal player had a greater impact on the team.
However, Mourinho's preferred back two of Terry and Ricardo Carvalho meant that Gallas would either have to be dropped or placed in one of the full-back positions.
The French defender, therefore, spent a decent amount of his last two seasons with the club playing at either left-back or right-back without any qualms.
Gallas was an important part of Chelsea's first Premier League win in 2005, and the defence of the title in 2006.
After falling out with the management at the club, he chose to move to cross town rivals Arsenal, in a deal which saw English left-back Ashley Cole go the other way.
Despite a bitter end to his Chelsea career, Gallas is regarded as a key figure in the club's success in the modern era, and is one of the few players who has experienced football at the Bridge before and after the arrival of Roman Abramovich.
Looking at the rich history of players that have arrived at the Bridge from the French League, and succeeded, Batshuayi is expected to have a similar effect with the club.
Blues fans will be eagerly following the Belgian's performances during the remainder of the Euros, in order to catch a glimpse of the talent that is set to play for the club next season.
Can Michy Batshuayi be a success at Chelsea? Let us know YOUR thoughts in the comment section below!