Beckham certain to return to San Siro
The Los Angeles Galaxy midfielder, who wants to play in Europe to try to secure his place in England's World Cup squad, had previously said the deal was 95 percent done.
"It's 100 percent certain. The only thing that is missing is the signatures but the agreement is complete," Galliani told Italy's Sky television.
Beckham is expected to stay at the San Siro from January until the end of the Serie A season in May, just as he did this year.
He has previously said he intends to go back to Galaxy following June's World Cup in South Africa, if selected by England coach Fabio Capello.
Media reports had linked the former Manchester United player with a return to the Premier League but the 34-year-old had always said another stint at Milan was his preferred option.