According to the Daily Mail the forward will take a 50 per cut wage cut for the opportunity at a second crack at the Premier League.
Last season on loan at Manchester United from Ligue 1 club AS Monaco, the Colombian international managed just four goals amid an injury hit spell.
JOIN THE DEBATE
Have Chelsea got a good deal with Falcao? Join the debate by becoming a GMS writer HERE: http://gms.to/haveyoursay1
Manchester United were reportedly shelling out around £285,000-a-week for the pleasure of Falcao at Old Trafford but he's believed to have agreed to accept around half that to play for Jose Mourinho at Chelsea.
The deal, which was confirmed by Chelsea earlier this week, sees Falcao join Diego Costa and Loic Remy in the Blues strike force.
And while Falcao is not the player he once was based on last season's evidence, it is certainly a move that makes the defending Premier League champions a formidable threat again next season.
Once regarded as one of the top three strikers in world football, Falcao suffered a brutal knee injury at Monaco and has struggled to get back to his previous form.
Now 29, he should be at the peak of his career but it's unlikely he will dislodge Costa from the starting lineup and is probably earmarked by Mourinho as a luxury option off the bench.
Like Manchester United, the report claims Chelsea also have an agreement in place with AS Monaco to purchase Falcao at the end of the season if he lives up to expectations.
Earlier this summer Mourinho said he would like the chance to help Falcao rediscover his top form.
The Chelsea manager said: "If I can help Falcao reach his level again, I will do it. It hurts me people in England think that the real Falcao is the one we saw at United."
What do you think Chelsea fans - a good deal at this price?