New Zealander Gatland, who has been in charge for only five games, saw the players complete a tournament clean sweep by beating France 29-12 at the Millennium Stadium on Saturday.
That came less than six months after Wales were knocked out of World Cup contention by Fiji as they failed to progress beyond the pool stage.
Edwards told BBC Radio Five Live's Sportsweek: "Warren has turned more or less the same squad into Grand Slam champions.
"It sounds easy and it looks easy, but Warren has been the difference between us being out with the empties and being up there and really enjoying this success.
"It is extremely special, especially after the position we found ourselves in at the World Cup."
Edwards also acclaimed the players, led to glory by captain Ryan Jones as Wales landed a second Grand Slam in four seasons.
"They performed well beyond our imagination," Edwards added.
"I didn't foresee Wales being crowned Grand Slam champions. But they deserve it and they've earnt it.
"I thought it would be a mixture of results this season, but Wales have been the most consistent side in the Six Nations.
"There seems to be a new-found confidence, and people seem to have their feet on the ground. Nothing appears to faze them.
"There's a confidence and a structure in the side, and everyone seems to know what they have got to do - and they are prepared to work extremely hard to do it."