Educated at St. Munchin's College and the University of Limerick, Staunton was capped for Ireland at Under-19, Under-21 and 'A' levels before he made his senior debut against Samoa in November 2001.
The 26-year-old has added three more caps, the last of which came during last summer's tour to New Zealand and Australia.
His last outing in an Ireland jersey was in November's 'A' international defeat to Australia at Thomond Park, and Staunton could have a big role to play for Ireland 'A' at May's Barclays Churchill Cup tournament in England.
Commenting on his move to London Irish, he said: "I've enjoyed my time at Wasps but I need a fresh challenge. London Irish has offered me the chance of that.
"I continue to have ambitions to play for Ireland so the more top level experience I can get, the better. I'm looking forward to starting the new season with London Irish," added the former Garryowen and Munster player.
London Irish's Director of Rugby Brian Smith, said: "Jeremy is an exceptional Premiership player who will bring a lot of valuable experience to us. He is a mature person and player whose best rugby is ahead of him.
"He is coming from a winning culture where he is a key decision-maker on the park - we will be looking to benefit from that."
London Irish will be the third English club Staunton has joined - he previously left Munster for NEC Harlequins.