Foxes snap up Coyne
Foxes boss Micky Adams was keen to bolster his goalkeeping options after Tim Flowers decided to retire and Simon Royce left for Charlton.
The 29-year-old Welshman has decided to leave Blundell Park after The Mariners suffered relegation down to Division Two last season.
Coyne will now be challenging Ian Walker for the number one spot at The Walkers Stadium, in the hope of tasting Premiership action.
"I am delighted that we have managed to get him," Adams told the club website.
"With Tim Flowers retiring and Simon Royce moving on to Charlton, securing another goalkeeper was a priority.
"We have agreed everything and he is signing for us subject to a medical. I believe he will be an excellent addition to our squad."
Coyne arrives at the club on a free transfer and will seal his move once he completes his medical.
The former Tranmere Rovers shot-stopper joined his new team-mates for the start of pre-season training, and joins Steve Howey, Paul Brooker and Riccardo Scimeca as the club's newest recruits.