The 37-year-old, who played for the Serie A giants from 2002 until 2012, will replace Massimiliano Allegri, who was sacked as head coach on Monday after a poor start to the season.
"I am retiring from football after 22 years," said Seedorf. "My aim is to dream again."
Milan are currently 11th in the Italian top flight.
They have won only five of the first 19 games this season, and are 30 points behind leaders Juventus.
Allegri's sacking came after Milan lost 4-3 to minnows Sassuolo on Sunday.
Former Netherlands midfielder Seedorf made more than 400 appearances for Milan, helping them win two Serie A and two Champions League titles.
He was also the first player to win the Champions League with three different clubs - Dutch side Ajax in 1995, Spanish giants Real Madrid in 1998 and Milan, in 2003 and 2007.
He has also played for Inter Milan and Sampdoria and, after leaving Milan, the Dutchman joined Brazilian side Botafogo in 2012 where he finished his playing career.
"This experience at Botafogo has helped me grow a lot and will no doubt help me in my next step as coach of AC Milan," Seedorf added.
"I wish Botafogo and my team-mates the best."