The 37-year-old Dutchman, who has no previous coaching experience, told a Rio de Janeiro news conference that he was retiring as a player. He left Milan for Brazil's Botafogo in 2012.
"This isn't a goodbye, we'll meet again," he said at Botafogo's stadium.
"All the experience I have gained in this year and a half at Botafogo is going to help me in my next venture, which will be as coach of Milan."
Seedorf will replace Massimiliano Allegri who was fired by Milan on Monday following a dismal run of results for the seven-times European champions.
The move to appoint Seedorf, who had a successful 10-year playing career at Milan, is something of a gamble although he is a hugely popular figure at the club and would arrive with a deep bank of goodwill.
The midfielder was the first player to win the Champions League with three different clubs - Ajax Amsterdam in 1995, Real Madrid in 1998 and AC Milan in 2003 and 2007. He has also represented Inter Milan and Sampdoria.
The former Dutch international won two league titles and an Italian Cup to go with the two Champions League victories during his time at Milan, which also saw him awarded the UEFA Best Midfielder Award in 2007.
Milan are currently 11th in Serie A after squandering a two goal lead in a 4-3 defeat at promoted Sassuolo on Sunday night. That left them 30 points behind leaders Juventus and 20 points off the final Champions League berth occupied by Napoli.
(Reporting by Andrew Downie, editing by Justin Palmer)
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