Milan sacked Massimiliano Allegri on Monday and will replace him with 37-year-old Seedorf, who won two Champions League titles with the Italian giants in a 10-year career at the San Siro.
Seedorf revealed the news at a press conference in Rio De Janeiro where he also stated he will be retiring from playing.
The Dutchman has been playing in the Brazilian league with Botafogo, but his agent has claimed that he has a release clause in his contract.
"I am here to announce that I will retire from playing after 22 years," said Seedorf.
"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 a team which has qualified for the (Copa) Libertadores.
"I leave an improved club, especially in terms of their mentality and team spirit.
"Yes, I will be the coach at Milan."
"Considering my relationship with the president (Silvio Berlusconi) when he called me yesterday I couldn't say no after 10 years spent there. My aim is to dream again."
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.
Milan are currently eleventh in Serie A after blowing a two-goal lead in a 4-3 defeat at promoted Sassuolo on Sunday. That left them 30 points behind leaders Juventus and 20 points off the final Champions League berth occupied by Napoli.
Carlo Ancelotti was Seedorf's boss at the San Siro and he believes the former Holland international midfielder has what it takes to succeed.
"Seedorf was my player, he has a very big personality," said Ancelotti, now in charge of Real Madrid. "He has the capacity and knowledge to do everything in the world of football. He is going to get experience in an atmosphere he knows very well.
"Milan have often made this type of decision, first Arrigo Sacchi who had no experience, then Fabio Capello... now Seedorf. Every time that decision has gone well for him. I wish him a lot of luck."