"Internazionale wishes Hernanes a very warm welcome to the club. The Brazilian midfielder's transfer from Lazio has now been completed and all the paperwork filed with Serie A," the club said in a statement.
"Hernanes has put pen to paper on a four and a half year deal that runs to 30 June 2018."
Earlier, the 28-year-old announced he was leaving Lazio.
"I have told the president (Claudio Lotito) I would like to go in the belief it is best for me as a professional," Hernanes said on his Facebook page. "I want to thank Lotito personally because he has always been fair with me but this is my choice.
"Thank you for the love which you have given me from my first day here until today and know that I will love you forever and will never forget you."
Lazio supporters staged a demonstration outside Lotito's offices in Rome against the decision to sell one of their key players.
On Thursday, Hernanes was seen crying with fans who pleaded for him to stay as he left the club's Formello training ground.
Inter are fifth in Serie A, 23 points adrift of leaders Juventus, and have won only one of their last nine games since Erick Thohir bought 70 percent of the club in November.
The Milan team travel to Juve on Sunday.
(Editing by Tony Jimenez) nL3N0L55FY
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