The 18-year-old playmaker has joined the Italian giants from Dinamo Zagreb, scuppering United's hopes of landing the youngster.
The Croatia under-21 star has been scouted by a number of Europe's top teams over the past few months, but Inter Milan have moved first to bring him to the San Siro.
The Serie 'A' club sold Philippe Coutinho to Liverpool earlier this month, and the signing of Kovacic is believed to be a direct replacement for the departed Brazilian.
The report claims Inter's £10m deal for the 18-year-old has been rubber-stamped, and it is now official.
Kovacic is one of a number of talented young Croatian stars - along with the likes of Alen Halilovic - and is expected to challenge for a first-team place almost immediately.
He made more than 40 league appearances for Dinamo Zagreb despite his tender years, helping them to win the league title in his first senior season.
He's also featured in the Champions League this season against Porto, Paris St Germain and Dynamo Kiev, and was nominated for the prestigious Golden Boy award for his performances last year.
His style of play has been compared to Lionel Messi and Wayne Rooney by Croatian pundits and there are high hopes for the teenager in his native country.