Van der Sar, who played in the Netherlands' 2-0 win over Romania in a World Cup qualifier on Saturday, has signed a two-year contract beginning on July 1. The transfer fee was not disclosed.
The 34-year-old is United's first signing since the club was taken over by American businessman Malcolm Glazer last month.
Van der Sar, who has made 95 international appearances, joined Fulham from Juventus for five million pounds in 2001.
United have struggled to find a long-term replacement for Danish goalkeeper Peter Schmeichel, who left in 1999 after eight years at Old Trafford during which they won the Champions League, five Premier League titles and three FA Cups.
Australian Mark Bosnich, Italian Massimo Taibi and Frenchman Fabien Barthez failed to establish themselves, and Northern Ireland's Roy Carroll and American Tim Howard shared the goalkeeping duties with mixed success last season.
United released Carroll and Spaniard Ricardo, their third-choice keeper, last month. Howard recently signed a contract extension until 2009.
Van der Sar made his name at Ajax Amsterdam, helping the Dutch club win the 1995 Champions League, before joining Juventus in 1999. He played around 70 matches in two seasons in Italy.