Hape will join on a two-year deal from Bath and is currently in Martin Johnson's England squad for the Six Nations.
The 29-year-old dual international appeared in all of last November's autumn internationals for England at Twickenham and made his eighth test start this month.
London Irish head coach Toby Booth said: "Shontayne is a player I have been very impressed with since his move to rugby union. He is physically very intimidating and his ability to offload out of the tackle will trouble any defence. We have a lot of young talent coming through the club and the experience that Shontayne brings will also help them to develop further."
Hape spent six seasons in rugby league playing for the Bradford Bulls and representing New Zealand Kiwis at international level, where he gained 14 caps.
He then changed codes in 2008 to move to Bath, where he signed a three-year deal, and he made his England debut last year in the tour of Australasia.