Milan, in their first season under coach Massimiliano Allegri, took an unassailable nine-point lead over bitter rivals Inter, champions for the last five seasons and the only team who could catch them before the start of the weekend.
Inter host Fiorentina on Sunday and have three matches left but, even if they caught Milan, Leonardo's side would still lose out on their head-to-head record which decides the title if teams finish level on points.
It was Milan's 18th Serie A title, pulling them level with Inter, although they are still nine behind Juventus.
"They gave us up for dead and they thought I was finished," midfielder Gennaro Gattuso told reporters as his team mates celebrated on the pitch at the Stadio Olimpico.
"Allegri deserves a mark of 10, he has been the architect of this success, he has kept the squad closely-knit." Unheralded Allegri, who until 2008 plied his trade in the lower divisions, was appointed in June after previous club Cagliari sacked him for talking to Milan.
"It's a beautiful moment which has arrived after seven years," added 35-year-old Dutch midfielder Clarence Seedorf, who was at the club in 2004 but will be out of contract at the end of the season.
"This squad will improve a lot after this win." Milan, who lost to Tottenham Hotspur in the Champions League last 16, have not been especially sparkling this term in what has generally been a weak Serie A but they have done enough thanks to the early season goals of Zlatan Ibrahimovic and a good defense.
Inter struggled at the start of the campaign with injuries and Rafa Benitez was sacked as coach in December after failing to fill the large shoes of Jose Mourinho, who led Inter to a treble last term before heading to Real Madrid.
A generally dire first half saw Milan passing the ball sideways and backwards while eight or nine Roma players protected their own penalty area.
Roma had the better chances on their occasional forays forward with Mirko Vucinic forcing a point-blank save from goalkeeper Christian Abbiati.
Alessandro Nesta also made a crucial clearance with the Montenegrin lurking behind him before Aleandro Rosi forced Abbiati into action again.
Milan, with Ibrahimovic returning from a three-match suspension, made a livelier start to the second half and Robinho hit the post almost immediately having shaken off Marco Cassetti.
Kevin-Prince Boateng flicked the ball agonizingly wide on the hour after being sent clear by Ibrahimovic, who shortly afterwards had a fierce effort parried away by Doni.
Despite chasing a place in the Champions League, Roma looked more than happy to settle for a draw.
The point took them into fourth place, which would earn them a place in the Champions League qualifying round, on 60 points, the same number as fifth-placed Lazio and one ahead of sixth-placed Udinese, who meet on Sunday.
Europa League hopefuls Palermo beat relegated Bari 2-1 in Saturday's other match.
