The Milan club, which is owned by Italian premier and media tycoon Silvio Berlusconi, announced on their website the player had agreed a five-year deal.

That will keep him at the club until the end of the 2007 season.

Both clubs confirmed earlier in the month that talks had been ongoing but Lazio reportedly turned down an initial offer of �17m. He is thought to have joined for �21m.

Nesta, 26, is regarded as one of the world's best defenders and was part of Italy's World Cup team this summer.

But the central defender, who started his career at Lazio, was plagued by a foot injury througout the tournament.

Milan, who have already signed Brazilian forward Rivaldo, turned to Nesta after failing to get Italy's other star defender Fabio Cannavaro from Parma.

Cannavaro, who had been in talks with Milan and Juventus, unexpectedly joined Internazionale.

AC Milan last won the league title in 1999. The defence is considered to be the team's weakest element, despite the presence of big names such as Paolo Maldini and Roque Junior.