The Corkman has also been capped 24 times by Ireland, most recently against England in Twickenham last Saturday, and was one of the outstanding performers in Ireland's 2009 Grand Slam success.
This led to him being named in the original 2009 British & Irish Lions touring squad. However, an ankle injury prevented him from taking part.
London Irish director of rugby Brian Smith said: "It is great to be announcing this week, just ahead of our St. Patrick's game, that a current Ireland international will be joining us for next season.
"Tomas will be a fantastic addition to our squad. He is a proven scrum half who has represented his country at the highest level.
"He will bring with him a wealth of experience and a winning mentality. We look forward to welcoming him to the club this summer."
Commenting on signing for the Exiles O'Leary, who is 28, said: "Joining London Irish presents a new and exciting chapter in my career and one that I am really looking forward to.
"I have thoroughly enjoyed my time at Munster and the Heineken Cup triumph in 2008 will always remain a particular highlight for me.
"I'm looking forward to working alongside Brian and the coaching team and testing myself in the Aviva Premiership and playing alongside a very talented squad at London Irish.
"I have been lucky enough to be part of some winning teams at both Munster and Ireland and I hope to have even more success as a London Irish player."