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The Times reports that Fekitoa's move to the struggling English side is expected to be announced "in the next few days".
The move also appears to wipe out hopes that the 26-year-old midfielder would return to New Zealand to have another go at making the All Blacks squad.
In an interview with the New Zealand Herald in September last year, Fekitoa said he was pondering the prospect of returning to New Zealand to have another shot at the black jersey.
"Many people believe I'm out but I'm too young to give up on that," he said.
"I want to play at the highest level again. I want to put my hand up and get picked. I know I'm not part of the plan now but who knows?
"If you put in the work, have the right mindset and enjoy your rugby, things will come. Test rugby is still up there, so hopefully I return and be competitive again."
However, it appears Fekitoa – who reportedly currently earns a salary of $700,000 at Toulon – has decided to continue his career in the Northern Hemisphere.
The former Highlanders centre made a shock move to Toulon in 2017 after playing his 24th All Blacks test against the touring British and Irish Lions.
Fekitoa will join his old All Blacks teammate Lima Sopoaga and former Hurricanes and Wellington captain Brad Shields at the Wasps.