Edwards' future at the club had been in doubt after he recently revealed that he expected to return from the World Cup, where he helped Wales to a fourth-place finish, as a "free agent".
And it is understood that Wasps, with whom Edwards spent 10 years, winning four league titles and two Heineken Cups, have held talks with the former Wigan rugby league star over what is an amicable departure with just over 18 months remaining on his current contract.
Edwards' exit from Adams Park is likely to put the focus sharply on the Welsh Rugby Union and the Rugby Football Union to act quickly to secure the services of one of the most successful coaches of the professional era.
Edwards worked on a part-time basis for Wales from the beginning of 2008, with Wasps allowing him to be available to link up with Warren Gatland's side for Test matches, but his contract with the WRU expired following Wales' defeat to Australia in their third-place play-off at the World Cup.
WRU chief executive Roger Lewis is known to be keen to ensure that Edwards and the remainder of Gatland's coaching set-up remain with the national side.
The RFU are due to discuss England's poor World Cup performance at a Twickenham board meeting tomorrow.
A possible outcome of the quarter-final exit to France could see team manager Martin Johnson retained but his backroom staff jettisoned, opening the way for Edwards to work with England after turning down a miserly offer to work with the Saxons four years ago.
However, any rapid progress on that front may well be halted by the ongoing reviews of the red rose's tumultuous time in New Zealand.
Another potential future home for Edwards could be with the Cardiff Blues. Ironically the Blues are without a full-time boss after Dai Young made the move to take over the director of rugby role at Wasps.
Gareth Baber and Justin Burnell are currently in temporary charge at Cardiff City Stadium.
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