The Scot, who works weekends in a Glasgow sports shop to make ends meet, contends that he has fulfilled his contractual obligations to Warren in six fights since winning the WBO super-featherweight title by beating Román Martínez in September 2010.
A statement from Warren's office on Monday said: "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. 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 and his manager, Alex Morrison, who informed Warren on 5 March they were terminating their business relationship, will contest that view, claiming significant sums are owed to the fighter.
Burns said: "For the last year or so there's been a few issues that needed sorting out, which never happened.
"Alec sat down and we decided that we had to do something. We decided that finding a new promoter was the best option. After speaking to Eddie, the future's looking good."
Hearn, meanwhile, plans to put Burns on a major bill in Glasgow on 11 May. He will announce an opponent next week and will unveil further signings this week and next.
Burns's signing with Hearn's Matchroom stable – revealed in The Observer on Sunday – follows the defection from Warren last week of the Commonwealth super-middleweight champion, George Groves.
The unbeaten Londoner marked his debut for Hearn with an easy stoppage of the Argentinian Dario German Balmaceda at Wembley Arena on Saturday night.
Burns was due to fight at the same venue for Warren on 16 March against the IBF champion, Miguel Vázquez, until the Mexican withdrew, complaining of a stomach complaint. The show was then called off but Warren says he will go ahead with the promotion on 20 April, headlined by Nathan Cleverly, who will defend his WBO light-heavyweight title against the mandatory challenger Robin Krasniqi.
Hearn revealed on Monday: "We've got 16 fighters at the moment who want to sign with us and, if I wasn't full up, I'd sign them all. I'm going to announce another signing on Wednesday, and after that we might have space for one or two."
He is in discussion with Sky Sports to expand his calendar from 20 fights a year to 30, and said: "That would give me a chance to sign [some] of these others. I've got four five amateurs that I could sign, if we had the dates, and there are half a dozen existing champions who want to join who I'd love to sign, as well. You can't sign them all. The large majority are [from one stable]. The amateurs are Olympians."
That leaves open the tantalising possibility that he may tempt Olympic super-heavyweight gold medallist Anthony Joshua to join, although it is more likely the first signing will be the exciting Welsh featherweight Lee Selby, the brother of London Olympian Andrew Selby. Hearn seemed to rule out acquiring Kevin Mitchell, whom Burns stopped in four rounds in his last fight, in September, and said a unification fight with the American WBC champion, Adrien Broner, may happen later in the year.
Burns said: "The first thing I said to Eddie when he was talking about opponents was I'd fight anyone he put in front of me. It didn't bother me.
"Whenever Adrien Broner does an interview now, my name seems to be thrown out. He wants to fight me more than I want to fight him. He's talked about moving up maybe to 147 to fight Paulie Malignaggi [in Las Vegas on 22 June], so we just need to wait and see what happens."
There is the possibility, also, of fighting Amir Khan, who is rebuilding his career after losing his world light-welterweight title last year.
"Somebody said I'm struggling to make lightweight, but that isn't the case," Burns said. "The next couple of years, I'm definitely staying at lightweight. But, if I was going to move up, I could make light-welterweight. If that big fight came along, I'd never say never. I'd like obviously to unify the lightweight title. These are the fights I want."
One fight he is not interested in is a domestic showdown with Scotland's former world champion Scott Harrison.
"Scott was in the paper at the weekend saying he wanted to fight me," Burns added, "that he'd be ready at the end of March. You know, I feel there are bigger fights out there for me. It would be a big fight in Scotland. He was a great world champion, but I feel there are bigger fights out there for me. I know Frank had spoken about maybe making it, and Alec mentioned it as well, but I think both of them they never had the goods on the fight."
Hearn views Burns's power-base as Scotland – "the sleeping giant", has he called it. "Scotland is the only place he'll be fighting in the near future," the promoter said, "and I think we can build him there, bring the big fights to Scotland."
He also suggested Burns may eventually fight Vázquez. "I don't think that'll happen in May, but that could be a fight for September, the second fight," Hearn said. "It's really about getting him a credible opponent, a tough fight in Scotland, pack the undercard with other Scottish fighters and see what we can do in Scotland."
guardian.co.uk © Guardian News and Media Limited 2010
image: © KWDesigns