The 26-year-old joined Irish in October 2005, and has so far made 33 appearances.
Irish rugby director Brian Smith said: "We are disappointed that Riki has decided to move on at the end of his contract.
"He has been a breath of fresh air at London Irish and we will miss him, but we do have some very talented midfield players in Mike Catt, Seilala Mapusua, Shane Geraghty, Gonzalo Tiesi, Barry Everitt and Nils Mordt.
"Riki's decision not to re-sign has come as a big surprise, so we will take some time to review our squad and decide if we will go after another big midfield signing.
"While we were able to match his financial demands, he has decided to leave for other reasons."