Earlier, he met chief executive Adriano Galliani to sign a contract until the end of the 2015/16 season.
Seedorf, who had been playing for Brazilian side Botafogo, announced on Tuesday that Milan had asked him to replace Massimiliano Allegri, who was sacked on Monday following a 4-3 defeat to lowly Sassuolo.
The Dutchman immediately abandoned his playing career to accept the offer.
He inherited a side languishing in 11th place in Serie A with only five wins all season, although they are the only Italian team still in the Champions League.
Many fans have blamed the crisis on the club's confused transfer policy, rather than Allegri, and there is widespread doubt as to whether Seedorf, who spent 10 years of his playing career at Milan, can turn the situation around.
His first match in charge will be at home to Hellas Verona on Sunday (1945).
(Reporting by Brian Homewood, editing by Pritha Sarkar)
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