"The operation went technically well. It lasted one hour, the minimum for this kind of operations," said professor Pierpaolo Mariani, who conducted the surgery at the Villa Stuart clinic.
"A four-month recovery period is realistic. I'll give him back to (Roma's) technical staff in a month."
The striker is to spend three days at Villa Stuart before beginning a rehabilitation that should see him available for the start of the next season.
Totti, 31, suffered a blow to his knee early in a home game with Livorno on Saturday, which finished in a 1-1 draw. He was stretchered off the pitch late in the first half, grimacing with pain after firing a shot from outside the area.
Mario Brozzi, Roma's chief medical officer, said that Totti suffered a partial rupture of the cruciate ligament in the right knee.
"I had two very serious incidents in two years. Before that I had never suffered any serious injury," Totti said shortly before the operation. "Unfortunately, this is part of football too."
In February 2006, Totti suffered a major fracture in his lower fibula that sidelined him for the run-in of the Serie A season. He has since played with a metal plate in his ankle.
This season, Totti is Roma's top scorer with 14 goals. He won the European Golden Boot in 2007 with 26 goals.
He retired from the Italian national team in 2006 after winning the World Cup with the Azzurri.