The Dutch midfielder, who is in his second season at Brazilian club Botafogo, was the leading candidate to replace Massimiliano Allegri, who was sacked on Monday.
"Considering my relationship with the (Milan) president (Silvio Berlusconi), when he called me yesterday I couldn't say no after 10 years spent there (at Milan)," Seedorf said in a press conference on Tuesday at Botafogo's headquarters in Rio de Janeiro.
He added, according to globoesporte.com: "This experience in the last year and a half has made me grow a lot and will help me in my next step, which will be as Milan coach."
Seedorf joined Botafogo in 2012 after a 10-year stint at the San Siro. Milan have yet to confirm his appointment.
The 37-year-old is the only player to have won the Champions League four times with three different clubs - at Ajax (1995), Real Madrid (1998) and AC Milan (2003 and 2007).
"I am retiring from football after 22 years," he said. "It has been a difficult night but I am satisfied by what I've achieved in my career and what I've done at Botafogo.
"My aim is to dream again. I wish Botafogo and my team-mates the best.
"The level has increased thanks to everyone and I'm certain that the club will be able to remain at a high level."
Seedorf inherits a team that is 30 points behind league leaders Juventus at the halfway stage of the campaign after Sunday's 4-3 defeat at Sassuolo.
That result brought to an end Allegri's three-and-a-half-year spell at the helm of the Rossoneri.
Seedorf could make his coaching debut on Sunday evening at home to Hellas Verona.
Former Sampdoria and Inter midfielder Seedorf has a coaching badge but no managerial experience, although former AC Milan coach and current Real Madrid manager Carlo Ancelotti does not believe that will be a problem.
"It's not the first time that Milan would make a choice like this one," Ancelotti said before Seedorf's announcement. "It happened with Arrigo Sacchi and with Fabio Capello and in both occasions, things went very well.
"I know Clarence very well as he was one of my players and has always shown great personality.
"I believe that he has the knowledge and the capacity to do anything he wants in football.
"He would face a new experience in a club he knows very well and this is important. I wish Milan and Seedorf the best of luck."
Allegri led Milan to a Scudetto and an Italian Super Cup in his first season in charge, 2010-11, but was enduring a frustrating campaign in Serie A before being dismissed.
Milan have won five and lost seven of their 19 league games and are 11th in the table and just six points clear of the drop zone.
The Rossoneri parted company with sporting director Ariedo Braida earlier this month to end his 27-year working relationship with Milan.
Back in December, the club underwent a board restructuring with club owner Silvio Berlusconi's daughter, Barbara, appointed as vice-president of the club.
Long-time vice-president and club administrator Adriano Galliani kept his job despite suggestions he might be shown the door and he has shared responsibility for day-to-day running of the club with Barbara Berlusconi, with Milan's ultra fans blaming poor leadership by the club's board for the Rossoneri's dismal season.
A statement from fans group Curva Sud read: "The Curva Sud wishes to thank Mr Allegri, who after a logical decision from the club, parts company with Milan.
"We wish to thank him for the Scudetto and for the qualification to the Champions League, but above all for the man he has proved to be!
"Now we wait with confidence to see what happens next, without forgetting that the total absence of a project for the future and a transfer market that has had little significance are the main causes of Milan's ailments!
"Let us not forget the uncomfortable seat that is shared by two (Adriano Galliani and Barbara Berlusconi) and the leadership that dampens the story of this club that is our life."