The 31-year-old centre made his England debut under Martin Johnson during the two-Test tour of Australia in 2010 before appearing in all five of England's RBS 6 Nations games the following year as they claimed the title for the first time in eight years.
Hape's last appearance came during England's World Cup win over Georgia in New Zealand, when he scored two tries, but Johnson's departure saw him fall out of favour.
The New Zealand-born centre was already sidelined with a knee injury and London Irish have confirmed he will not feature for the club again before his departure.
"We'd like to thank Shontayne for his time with London Irish," said the Exiles' director of rugby Brian Smith.
"We wish him the very best of luck for his future career with Montpellier.
"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."