He started the match against Rubin in Kazan, so he's cup tied.
Time will tell how good this signing will be.
On one side he's cup tied, hasn't played regularly for 18 months, highly inconsistent, has high wages (3.5m eur a year, of which Milan will have to pay half for this season) and Milan will surely be 2nd or 3rd in serie A, with or without him, but don't stand a chance to win serie A.
So, as far as this season goes, he might be useful only as a card to be played right before the CL matches and give a rest to Dinho or Beckham. Since losing or winning those few pre-CL matches won't change much for Milan (and I doubt Mancini can make a difference between winning those matches or not anyway) there isn't much logic in getting him.
Maybe they count on him for the next season. 6.8m eur for half of him.
He'll be 30 this summer, he has high wages (something that put Milan in this tough position is paying high wages to +30 year olds) and Milan will have to convince Inter to let Mancini play for Milan next season.
Also, if Mancini won't get much playing time this season (and will he? With Dinho, Beckham, Seedorf, soon Pato will be back, will he play enough?) then will Milan decide to buy him next summer? If they don't, what's the use of Mancini this season?
Many question marks so as I said above, time will tell. But right now it doesn't look like a very logical move.