Hape, 31, becomes the latest big name player to leave the Exiles, following Delon Armitage and Nick Kennedy in moving to French club rugby.
Shane Geraghty has been linked with a return to London Irish and director of rugby Brian Smith confirmed he has already lined up Hape's replacement.
"We'd like to thank Shontayne for his time with London Irish. We wish him the very best of luck for his future career with Montpellier," Smith said.
"London Irish has some fantastic young and talented backs who have greatly benefited from training and competing alongside him.
"We look forward to watching those guys in action for the rest of this and next season and to announcing Shontayne's replacement very shortly."
Hape joined London Irish from Bath after the 2011 Rugby World Cup.
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