Beckham will join Milan on 7 January, the Italian club stated on their website this evening.
Milan have not disclosed the length of Beckham's loan contract but the England midfielder has stated he will return to the United States in time for the start of the Major League Soccer season, which is expected to begin in late March or early April.
Milan director Umberto Gandini confirmed Beckham's stay in Italy would be a short one.
And the Serie A giants do not expect any opportunity to arise which would allow them to sign the 33-year-old permanently.
Beckham is seeking to maintain his match fitness to ensure he stays in the England squad, as he closes in on a record number of caps for an outfield player.
The former Manchester United and Real Madrid midfielder has 107 caps, one behind the late Bobby Moore who led England to their 1966 World Cup triumph.
He hopes to retain his place in coach Fabio Capello's squad with a view to probably bowing out after the 2010 World Cup.
Capello has indicated he will only select players who are active with their clubs, and with LA Galaxy now in their off-season, Beckham risked being left out for upcoming games, including the proposed friendly against European champions Spain in February.
Gandini told Sky Sports News: "The deal will be as long as David wishes.
"I think his commitment to MLS and Los Angeles Galaxy will take him back after a couple of months.
"I think he will have to go back to Galaxy by the time the MLS starts, and training before that."
Asked about the potential for Beckham staying with Milan on a longer-term basis, Gandini said: "No, David is committed to the Los Angeles Galaxy and the MLS.
"He thanks them for the opportunity to let him train and work with us, we're very happy for that.
"Only David knows his future, but for sure he has a commitment to go back to the MLS and I think he will fulfil that."
Beckham will join a star-crammed squad at Milan, with the likes of Andriy Shevchenko and Ronaldinho soon to be team-mates.
"The players understand we are the premium brand," said Gandini.
"We are a fantastic club, one of the best clubs in the world.
"The fact they want to play with us is a great achievement.
"David Beckham will come to our club where he will have a lot of people and a lot of players that have his ability and status so I think it will be very beneficial for him and the English game."
Beckham is not certain to feature regularly for Milan, with nothing in his loan contract stipulating he will play in a specific number of games.
Gandini said: "David is coming as a Milan player and he will train with the other Milan players and the selection will be up to the coaches."
Capello expects David Beckham will prove a "great acquisition" for Milan, the England coach's former club.
Capello has worked with Beckham at Real Madrid and England and has been impressed by his work-rate.
Speaking before the deal was completed, Capello told Milan's World Business Forum by satellite: "If Milan sign him they will make a great acquisition.
"He is a very focused lad. He is a professional.
"When I left him out of the team in Madrid because he had signed the contract with the Los Angeles Galaxy, he continued to come to the pitch to train and I put him back in the team."
Talks over Beckham's future were originally scheduled for next week, but the player's representatives and Milan vice-president Adriano Galliani met this afternoon to thrash out the transfer.
The former England captain had been a target of Milan before, in January 2007, but opted instead to move to Los Angeles from Real Madrid.
In a joint statement tonight, Milan and LA Galaxy confirmed Beckham would return to the United States for training before MLS begins, which suggests he will spend just two months back in Europe.
Former AC Milan striker Luther Blissett expects Beckham's move to have a positive impact on his new club, and on the England team.
Blissett told Setanta Sports News: "I'm glad they've sorted it. For England and for Beckham it's a very good move.
"Having somebody of the calibre of David Beckham fit and available to play for England is good for everyone.
"Milan have always been very good commercially, they obviously recognise David Beckham as a great acquisition for the club."
Writing on his blog, on davidbeckham.com, Beckham this week admitted he was looking forward to joining Milan.
He explained: "One of the reasons I want to train and play in Milan for a few months is the fact that the MLS season doesn't run as long as the European season and having played most of my career in Europe, my body has been trained and geared not to have that amount of time off.
"Obviously, I will be honoured to be given the chance to train and play with the likes of Ronaldinho and Kaka, but it also gives me the chance to keep my fitness up and carry that on for when I come back to the Galaxy for the new MLS season."
He rubbished suggestions he had bought a house in Milan and denied planning to purchase a jet, and also confirmed LA Galaxy remain his priority.
"Next season is an important one for the Galaxy," Beckham remarked.
"We haven't been in the play-offs for three years now and for a team like LA Galaxy we all know that isn't good enough.
"(Head coach) Bruce Arena will also have had the chance over the past few months to get used to the squad and, with his experience and previous success, he'll want to make sure that we're up there competing next year."
Galaxy boss Arena has given his blessing to Beckham's transfer.
Arena had described the deal as "an odd proposition" last week and questioned whether the MLS and Galaxy would benefit.
However he has become convinced Beckham is making the right move.
"Clearly I think this is an ideal situation for David," Arena told Sky Sports News.
"It can benefit David, it can benefit England, it can benefit the LA Galaxy and hopefully it benefits AC Milan as well."
Arena expects the 2009 MLS season to start on March 19, and he stressed Beckham will be involved.
"David will be back and have a couple of weeks of training with our team and will be ready to really kick off in a good fashion in 2009," Arena said.
The former United States head coach recognises Beckham's desire to stay involved and active with England.
"I can't speak for David but what motivates any top-level footballer is the fact that playing for your national team is the greatest honour," Arena said.
"And having the potential to play in another World Cup is every player's dream.
"I think these are the things that motivate him."
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