The 25-year-old tighthead prop joined Leinster from school before moving across to Galway where he spent two years with Connacht, making 50 appearances for the westerners. He moved back to Leinster in the summer of 2011.
Hagan was drafted into the Leinster Academy as an 18-year-old in 2005 and was capped, provincially and nationally, through the age grades.
In 2007, he was a member of the Ireland team, coached by Eric Elwood, that captured the Under-20 Grand Slam.
London Irish director of rugby Brian Smith said: "Jamie Hagan is a future Irish Test player, he's cut his teeth in the RaboDirect PRO12 and is more than ready to launch his Aviva Premiership career.
"He's a tough, uncompromising prop coming into his prime and he'll add more steel to our tight five. Jamie's rugby talent and Irish heritage make him a perfect fit for the club. I'm genuinely delighted that he's committed to London Irish for the next three seasons."
The Balbriggan man, who has made two appearances for the O2 Ireland Wolfhounds, said: "I'm looking forward to moving across to England and joining London Irish. They are a team with a rich heritage and proud Irish traditions which will really suit me.
"I would like to thank Leinster for all they have done for me and wish them well for the future. I look forward to joining London Irish next season and getting stuck in to Premiership rugby."