Borini, who worked with Rodgers on loan at Swansea City last year, has joined on a long-term deal after passing a medical at the Premier League club. No fee was given but British media said the deal was worth up to 11 million pounds.
The 21-year-old, who scored 10 goals in 26 appearances for Roma last season, was part of Italy's Euro 2012 squad which reached the final before losing 4-0 to holders Spain although he did not play in any of the matches.
"Fabio fits the model of what we're trying to do in building not only for now, but also for the future," Rodgers said of his first signing for the Anfield club who will wear the No. 29 shirt after asking for his lucky number.
"He's a big talent, 21 years of age, he scores goals, and his passion, focus and concentration is a very important part of his game - and a big part of what you want from a player.
"He's technically strong, he's a good finisher with both feet, he can play central or on the sides in a 4-3-3 up front, he's quick, and he's tactically very good," said Rodgers.
Borini added on the club's website: "It's a top club that has won a lot of trophies in the past - and will do so in the future we hope as well.
"I've got the trust of the manager and the club, which for me is very nice and I'm proud to be here."
Asked if Rodgers was they key reason for joining Liverpool Borini said: "He was very important. I wouldn't say it was the key, but most of it came from him."
Maxi, who moved to Anfield from Atletico Madrid in January 2010, netted 17 goals in 73 appearances for Liverpool.
"I have tried to give everything every day that I was wearing the LFC crest," he said. "It has been a great honour to defend this shirt during two and a half years."
The 31-year-old international began his career with Rosario-based Newell's before joining Espanyol in Spain.
