Swansea have secured Borini on loan until the end of the season.
Boss Brendan Rodgers told the club's official website: "I'm delighted with the signing.
"He's a player I tried to get earlier in the season but because of complications with his contract at Chelsea and the fact he was in and around the first team, he didn't get permission to go out on loan.
"He's a young player with great potential. He's got intensity, passion and a natural goalscoring ability.
"I worked with him in Chelsea's youth and reserve team and I firmly believe he will help us a great deal during the run-in."