The former Netherlands international returns to Milan, where he won two Serie A and two UEFA Champions League titles, to take over the role left vacant by sacked coach Massimiliano Allegri.
With the European giants sitting 11th in the league - 30 points off first-placed Juventus - Seedorf said it was a huge opportunity.
The 37-year-old retired from Brazil Serie A club Botafogo to take up the position.
"I am very happy to have this opportunity. I am keen to end in style my adventure here in Brazil which has been wonderful to me, before starting my new adventure in Italy," Seedorf said.
"I will soon be able to answer all questions about the future. I feel honoured and motivated. To be in a great club like AC Milan is a dream for everyone who wants to become a coach."
Seedorf thanked Botafogo and the people of Rio de Janeiro and said he hoped Brazil would do themselves proud hosting the 2014 FIFA World Cup.
"There have been a lot of positive things, and I have to thank Rio, I have to thank Brazil," he said.
"I have to thank all of you that are here today, and those that aren't here as well - part of the press - because I've been embraced in a certain way right from the start. And of course, it's not goodbye.
"I hope that Brazil will be able to have an unforgettable World Cup. And that the Brazilian squad will be able to honour the Brazilian colours to the world."
Botafogo president Mauricio Assumpcao said it would be a huge challenge to replace Seedorf, but wants a player of similar calibre.
"To find a player who is similar to Seedorf, it's going to be hard. I think this is the challenge we have here now," he said.
"I think it would be difficult to find someone who can bring everything that he brought to Botafogo."
Milan caretaker coach Mauro Tassotti, who will lead the side in their Coppa Italia clash against Spezia on Wednesday, backed Seedorf to be successful.
"There were top players who became great coaches and other top players who tried a career as a coach for one year or two and then stopped because they realised they weren't fit for the job," he said.
"We will see Clarence Seedorf at work, we know he definitely has the personality and the skills needed because he played football at the top level until yesterday."
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