Italy playmaker Montolivo, 27, joins the Rossoneri on a free transfer after seven years at La Viola, while veteran Dutchman Van Bommel returns to his former club on a one-year contract.
"Next season Montolivo will arrive and he is a very talented player with great technique,” Milan coach Massimiliano Allegri told his club's TV channel.
"Milan will remain competitive next year and we must continue the work we started last season. We need to begin again with great enthusiasm."
The 35-year-old Van Bommel joined Milan from Bayern Munich in January 2011 and said he would like to return to the club as a coach.
"I am leaving Milan and going back to Holland," he told Sky Sport Italia. "Maybe one day I’ll return as a coach.
"Life is like that, at a certain point you have to move on. When I arrived here, everyone told me this club was like a family. I have to say, it was all true."
Van Bommel's exit is part of a exodus of veteran Milan midfielders, with Clarence Seedorf also expected to join Gennaro Gattuso in leaving the club this summer.
Striker Filippo Inzaghi and defender Alessandro Nesta have also announced their departures from the San Siro, while full-back Gianluca Zambrotta could also leave.
Last year's Serie A champions, Milan will be runners-up this season after a 4-2 defeat to city rivals Internazionale last weekend handed Juventus the title with one match to play.
They were widely expected to rejuvenate an ageing side, with several more new signings set to be completed in the coming weeks.