“I am delighted that we have managed to get him," Foxes boss Micky Adams told the clubs official site.
“With Tim Flowers retiring and Simon Royce moving on to Charlton, securing another goalkeeper was a priority.
"Danny is a very experienced ‘keeper and has always done very well for Grimsby. And he also has international experience for Wales.
“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."