Boss Massimiliano Allegri revealed the Bosman pair were on their way yesterday.
"Seeing as we are a club who like to keep people informed, I'll give you some news today," Galliani stated yesterday afternoon.
"We have signed Mexes and Taiwo, two players who we will be counting on. Now we'll try to strengthen the side further, with the Champions League being our objective for 2012.
"Our target for this term was to break Inter's hold in Italy and, as you can see, we did that.
"However, although the Scudetto is of absolute importance, I can confirm that next season Milan will try to regain the Champions League."