The Welsh Rugby Union have confirmed that the controversial "Gatland's Law" will be changed to follow the selection model enforced by Australia, meaning that any players based outside of Wales will be eligible to play for the national team providing they have received at least 60 caps.
Biggar now has 56 caps to his name and should cross the 60-cap barrier before he leaves the Ospreys at the end of the season to move to Franklin's Gardens, but the 28-cap Webb looks certain to miss the 2019 Rugby World Cup despite Toulon's claim last week that that "a fair deal has been found in good faith with regard to his national selection in the interest of both parties".
Ross Moriarty, now at Gloucester, has a decision to make at the end of the season when his contract expires.
That means from next season he will not qualify to play for Wales if he goes through with the deal.
"I still very much want to play for Wales this season and hope I can gain selection for the autumn worldwide squad".
The introduction of this new policy means the previous one - nicknamed "Gatland's law" has been scrapped.
George North, Jamie Roberts and Taulupe Faletau all play outside Wales and have more than 60 caps.
Biggar has 56 caps but he is likely to hit the 60-mark this season, with Wales having four autumn Tests and then a Six Nations campaign.
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New Zealander Gatland, who has been in charge of Wales since late 2007, will leave his post after the 2019 World Cup in Japan. No, I wouldn't. It is not about me or the national team, it is about what is the best thing for Welsh rugby.
Current Wales assistant coach Rob Howley, who has twice stepped up to the lead coach role for season-long stints when Gatland has been on Lions duty, could be in the frame as a successor, while Wasps rugby director Dai Young also has his admirers.
Phillips said: "Whatever contract that a player is in today, that contract is protected".
WRU chairman and former Wales fly-half Davies says the board are pleased with their search so far and are confident they will appoint the right man when the time comes.
'The existing policy worked to an extent but it has not worked well enough, ' he added.
"A policy's been agreed on with the regions and the union and Rhys has made a decision to sign a pre-agreement for Toulon for next season, which means he won't reach the criteria in terms of playing the number of caps to be selected for Wales".
'It was quite complicated. There are market forces outside of Wales. We want to make it simpler.
"There is pressure on players to make what is the best decision for themselves and in the future".