Matchroom's Eddie Hearn announced that the two-weight world champion will fight for him on May 11 at a yet to be determined venue, with Burns keen to fight in Glasgow.
Warren and his W. Promotions Limited company responded with the following news release.
"Since being promoted and managed by Frank Warren, Ricky Burns has earned just approaching three quarters of a million pounds and has had seven world title fights in just over two years," it read.
"Ricky Burns is under binding promotional and management contracts. Following the announcement by Eddie Hearn that Ricky Burns has signed with him, W. Promotions Limited and Frank Warren are suing Burns for substantial damages."
Burns, whose last bout was a comprehensive WBO lightweight defence against Kevin Mitchell in Glasgow in September, follows unbeaten Commonwealth super middleweight star George Groves in leaving Warren for Matchroom.
Groves delivered an uncompromising third-round stoppage of Dario Balmaceda in his first contest as a Matchroom fighter on Saturday.
"I’m delighted that my future has been resolved and I'm really looking forward to the next chapter of my career," said Burns, 29.
"It’s been a frustrating time since the Kevin Mitchell win in September but now I’m just focused on May 11 and putting in a great performance.
"I would love it to be in Glasgow – my last two fights were there and the atmosphere was just electric. I’ve got great fans in Scotland and it means a lot to box in front of them."
Hearn added: "I’m delighted to welcome Ricky Burns to the team. Ricky is an outstanding fighter and a hugely popular sporting figure in Scotland."
Meanwhile Warren stated that his Wembley Arena promotion on Saturday April 20 will go ahead regardless.
WBO world light-heavyweight champion Nathan Cleverly headlines the show in a title defence against Robin Krasniqi, while Londoner Kevin Mitchell makes his comeback in a 10-round lightweight contest.
Subject to the return of his British Boxing Board of Control licence, heavyweight Dereck Chisora will also make his long-awaited return to the ring, while Liam Walsh will defend his commonwealth super-featherweight title.
W. Promotions stated that a further major championship title fight will be added to the card, with details to follow shortly.