Higuain will be reunited with Sarri, who managed the 31-year-old at Napoli and made him his top target in the January transfer window.
After spending the first half of the season in a disappointing loan spell at AC Milan, Higuain admitted he was keen to move to Stamford Bridge.
“It’s a team I’ve always liked that has a lot of history, a wonderful stadium and they play in the Premier League, a league I’ve always wanted to play in.
“I now hope I can give back that trust Chelsea have shown me out on the pitch. I can’t wait to start and I hope to adapt as soon as possible.”
Higuain had scored just once in his last 12 appearances for AC Milan.
But the former Real Madrid star, who will wear Chelsea’s No 9 shirt, is expected to recreate the fruitful relationship he had with Sarri in their one season together at Napoli in 2015-16.
He scored 36 league goals in 35 games for Napoli, breaking the Serie A single-season record.
Sarri was desperate to land a quality forward after enduring a series of frustrating results due to Chelsea’s inability to kill off their rivals.
Chelsea’s problems up front forced Sarri to play Belgium star Eden Hazard out of position as a striker rather than in his preferred position on the flanks.
Hazard’s form has suffered as a result and Sarri will hope Higuain’s presence will spark a revival in Chelsea’s fortunes, while allowing Hazard to return to the role he has filled so effectively on the left wing.
Chelsea director Marina Granovskaia added: “Gonzalo was our No 1 target in this transfer window and arrives with a proven record at the highest level.
“He has previously worked with Maurizio to great effect and is familiar with how the coach likes to play.
“This was not an easy deal for us to do because of the numerous parties involved, but we are delighted we were able to make it happen and we look forward to seeing the impact Gonzalo will make for us in the second half of the season.”
Chelsea play Tottenham in Thursday’s League Cup semifinal second leg at Stamford Bridge, bidding to overturn a 1-0 deficit to reach the February 24 final.
The Blues had until 12 pm to register Higuain for that match, but instead, he will have to wait for his debut, which could come against Sheffield Wednesday in the FA Cup fourth round on Sunday.
If not, Higuain could feature when Chelsea travel to Bournemouth in the Premier League on January 30.