The 29-year-old was unveiled as Hearn's latest recruit at a press conference in London yesterday, after he joined Commonwealth and British super-middleweight champion George Groves in leaving long-term promoter Frank Warren.
However, with Warren adamant the Scot is still under contract to him and maintaining Burns' next fight will be a revised date with Miguel Vazquez on April 20, litigation does not seem far away.
But Burns said: "I am just delighted everything has now been settled. I just want to get my career back on track and I believe I can do that with Matchroom. To say I feel I have been let down over the last year is putting it mildly but now I just want to look forward, starting with May 11.
"Eddie Hearn is confident he can bring the big names to Glasgow and that is where I want to be fighting. No names have been mentioned yet but I'm just looking forward to getting back in the ring and staying busy."
With Hearn confirming he is satisfied that his signing of Burns will withstand any challenge, the WBO lightweight champion's new promoter was clear about his targets for the Scot.
He said: "The short-term target is May 11 in Glasgow, the long-term target is for Ricky to unify the lightweight division, all on the Sky TV platform. We are delighted to have signed Ricky up and the plan is to get him back fighting in Scotland where he should be fighting.
"We have two venues booked for May 11 and then I would like to have Ricky back in action in September and then again in December. There are some huge fights out there for Ricky and we look forward to launching his career with Matchroom in May with a massive night."