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.
"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."
"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."
"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."
"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."
