The right-back has signed a four-year contract worth around £45,000 a week after tax at Stamford Bridge.
"I'm delighted to be a Chelsea player and can't wait to get started".
"It was clear Alonso had had a very good season for Fiorentina and really fitted the brief of what Antonio Conte wanted".
The Serie A club confirmed the deal was done shortly after the transfer window closed on Thursday night.
The 25-year-old was a regular in Torino's starting line-ups after arriving from Atalanta in July 2015.
He is well known to Chelsea boss Conte, who called him up to the senior Italy squad during his time in charge of the Azzurri and will hope he can quickly adapt to the Premier League. After Kante's move to Chelsea last season, where he won PFA Player of the Year, Drinkwater has followed his former teammate's footsteps.
China Rejects New US Sanctions Against Venezuela, Calls for Internal Solutions
"No military actions are anticipated in the near future", said U.S. national security advisor HR McMaster. That could choke off access to NY debt markets and raise the risk of Venezuela being forced into default.
Chelsea have signed defender Davide Zappacosta from Torino on a four-year deal for an undisclosed fee.
Drinkwater played a big role in Leicester's incredible title-winning campaign of 2015/16.
He is also relishing working under countryman Antonio Conte.
The Premier League champion is said to have paid $A41million plus €2m in bonuses to secure Zappacosta's signature.
"We are very pleased to be able to bring him to the club and believe he will become an important member of the squad".