The Dragons confirmed on Wednesday that flanker Lydiate, last season's Six Nations player of the tournament, will take up a contract "with an undisclosed European team".
Lydiate is currently sidelined after suffering a serious ankle injury earlier this season that ruled him out of Wales' entire autumn schedule of Tests against Argentina, Samoa, New Zealand and Australia.
Dragons rugby director Robert Beale admitted the Welsh region could not compete financially with what 24-year-old Lydiate had been offered elsewhere.
"We are obviously very disappointed that Danny has decided to leave the Dragons," Beale said.
"He has been a key part of our set-up for several years and is popular with both the players and the coaches.
"I can assure our supporters that we did all that we could to retain Dan's services, but we simply cannot compete with the offers which have been put on the table."
The chances are that Lydiate, who made his Wales debut three years ago, will follow the current trend and head to France.
Several of the current Wales squad, including Lydiate's former Dragons colleague Luke Charteris, scrum-half Mike Phillips, prop Gethin Jenkins and utility back James Hook, ply their club trade in France, while centre Jamie Roberts is set to join Parisians Racing Metro next term.
There have been issues, though, with player availability for international fixtures.
The Wales management were able to reach agreement with Perpignan for Charteris to play against Australia last weekend, although in return he missed the autumn opener against Argentina, while Hook and Bath prop Paul James were unavailable for the Wallabies fixture.
Lydiate, who hopes to make a playing return later this season, would command a significant salary as one of Europe's leading players.
Fitness permitting, he is a prime candidate to make the British and Irish Lions Test team in Australia next summer that will be coached by current Wales boss Warren Gatland.
Lydiate has been a Dragons player since 2006, and he overcame a serious neck injury the following year to resume a career that has seen him develop into a back-row performer of the highest calibre.
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