The former Netherlands international has been heavily linked with the role following the sacking of Massimiliano Allegri on Monday.
Allegri paid the price for a dismal season for Milan, who sit 11th in Serie A after 19 games and were beaten 4-3 by newly promoted Sassuolo on Sunday.
He told a press conference on Tuesday: "I am here to announce that I will retire from playing after 22 years.
"It has been a difficult decision, but I am satisfied with what I have achieved in my career. Here at Botafogo I am happy because I leave the team with qualification to the Copa Libertadores.
"I leave an improved club, especially for their mentality and team spirit.
"I will be the coach at Milan.
"This experience of the last year and a half has made me grow up a lot and will help me in my next step, as coach of Milan, who have hired me in a manner both elegant and correct."
Now Seedorf has the task of saving Milan's 2013-14 season, which is in danger of ending in mediocrity.
