The Barcelona president was locked in talks with the Rossoneri's vice-president, Adriano Galliani, on Monday and Tuesday before emerging with a deal finally sealed.
Manchester City's offer had been much higher, but Ronaldinho had always wanted to go to Milan and from then on it was a case of negotiating with the Serie A side.
Barca appear to have lowered their demands from earlier in the summer after new coach Pep Guardiola stated that the player was not part of his plans.
From then on it was difficult for the Blaugrana to consider holding out for their highest valuation and in the end a deal was struck with Milan that suits all three parties.
Satisfied
"We have reached the principle of an agreement and Ronaldinho will go to Milan to have a medical with the club," Laporta told reporters."I want to thank the effort made by Milan and the player in order for us to be able to reach this agreement. Everyone has done what we had to do."