The 31-year-old, who is trying to guide the Chiefs to the playoffs for the sixth consecutive season, doesn't believe he'll have another shot at Super Rugby.
He'll likely retire after completing his stint in France with Oyonnax, who have recently earned promotion to the French Top 14 championship.
Also leaving the Chiefs are All Blacks halves Aaron Cruden and Tawera Kerr- Barlow, winger James Lowe and coach Dave Rennie.
"I wanted to leave on my terms, and having won a couple of Super Rugby titles with the Chiefs," Elliot said.
"I feel I've accomplished all I can in New Zealand at this stage."
However, the nine-time Maori All Black is keen to play one final game for the Maori against the Lions when they clash in an "unofficial fourth test" in Rotorua on June 17.
"It's a team I hold dearly," Elliot said.
"I don't know if they're going to go for experience or someone a little bit younger with an eye to the future, but hopefully they'll go for an older statesman."