The Blues ended months of speculation on Monday as they confirmed their selected successor to temporary instalment Guus Hiddink.
Ancelotti will now take charge at Stamford Bridge for the start of pre-season training at the beginning of July and the Italian has already targeted success in the UEFA Champions League.
But Milan, who agreed to end the 49-year-old's contract 12 months ahead of schedule by mutual consent, say that they could have stopped their former chief from moving to England on a three-year deal.
"He told me about it the day he signed, but it remained dependent on him being allowed to leave Milan," Galliani said, referring to Ancelotti's pre-contract agreement with Chelsea.
Evaluate"We could have said to him that he had to stay, but we evaluated everything and thought that it is maybe better for Carlo, the club and for everybody like this.
"We did not publicise it back then because we had an agreement that we would wait until after the final game of the season. Now we have moved on."
Galliani, though, is adamant Ancelotti was not tempted to the Premier League by the wealth of Chelsea and owner Roman Abramovich.
"Carlo never asked us for a contract extension and he never asked for a pay rise," he said.
"He never asked us for anything. Every decision which was made was taken in total concordance with the club."