The 26-year-old Jamaican international has penned a one-year deal with the Shrimps as they prepare for a first season in League One.
Leigh progressed through the youth ranks at Manchester City before going on to play for clubs including Bradford City, Bury, NAC Breda and Aberdeen.
His signature was announced as the Morecambe players approach the end of their pre-season training camp in Worcester.
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“It’s been good to get to know people in a setting where we’re all together, day after day, getting training under our belts,” Leigh told the club website.
“When speaking with the gaffer, he has a real idea of how he wants to play and where he wants the club to go and himself, his players so he was really clear and ambitious, and I like that a lot.
“I’ve been unfortunate with injuries so I’m looking forward to putting them behind me and really propelling forward.”
Leigh becomes the club’s seventh permanent signing of the summer and 10th overall, taking the loan arrivals of Alfie McCalmont, Josh McPake and Callum Jones into account.
The full-back, who can also play in midfield, has been on Robinson’s shopping list in the past.
“He’s a boy I’ve tried to sign two or three times at Motherwell and wasn’t able to get him, but he comes with good pedigree,” the manager said.
“He’s had injury problems so that’s probably the reason we’ve got him, otherwise he’d be playing at a higher level so it’s a case now of keeping him fit, working slowly with him at the moment and getting him back to full fitness and I think he’ll be a big asset to us.
“Greg is versatile, he can play left-back, he can play in midfield as well and he gives us that pace and energy.”
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