Edwards' 11-year stay with the Grand Slam champions will come to an end after this autumn's tournament, when Warren Gatland will also stand down as head coach.
Defence coach Edwards was set to leave rugby union in favour of a return to league as coach of the Wigan Warriors when his contract expires at the end of the tournament, before a dramatic late U-turn.
He has now been offered a four-year deal by France with other options, including a role with England, also a possibility.
Edwards said: “After more than 10 years with Wales this has been an incredibly difficult decision to reach, but I won’t be renewing my contract.
“I would like to thank Warren and the WRU for the opportunity I have had working with the national team.
“We have won four Six Nations titles during my time with Wales, but I sincerely hope and believe that the best days are yet to come and I am fully focused on seeing what we can achieve in Japan.”
Gatland has welcomed the clarity on Edwards' Wales future, although speculation over his destination after Japan 2019 will persist.
The Kiwi admitted earlier this the week that the uncertainty was in danger of becoming a distraction as Wales look towards the start of their World Cup preparations this summer.
"Shaun has been an important part of the Wales set up over the past 11 years for what has been a hugely rewarding time for Welsh rugby," Gatland said.
"It's pleasing that we can draw a line under the speculation regarding Shaun's future with this announcement and we can look forward to preparing the squad for the RWC and the tournament itself in Japan later this year."
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