Edwards first worked with Gatland at London Wasps and has been part of the New Zealander's Wales set up since 2008.
Both men have been linked with a second successive Lions tour next year, although Gatland is likely to miss Wales' own trip to Australia this summer.
Gatland broke both his heels when he fell off a ladder at home and Rob Howley has since been named as caretaker coach for the three-Test series with the Wallabies.
Edwards is hopeful his boss can still play some part in the tour, though, especially as he believes there is no better coach in the global game.
"For me he is the best coach in the world and you are going to miss someone of that experience," said Edwards.
"Hopefully we can do him proud. You always want your boss around and you always want that experience around you."
Wales take on the Wallabies in Brisbane, Melbourne and Sydney on June 9, 16 and 23 as they look to build upon their second Grand Slam success under Gatland and Edwards.
Edwards will combine his international commitments with a new one-day-a-week role as defence coach at London Irish after Wales return from Australia and the former rugby league star can't wait to get started at the Madejski Stadium.
"I've looked at the record of London Irish and they lost a lot of close games this year and if they can turn them into victories they will be challenging for a play-off spot. Certainly we want to be in a Heineken Cup place," Edwards told Sky Sports News.
"It was only a few years ago that London Irish narrowly lost in the grand final against Leicester, so it's an ambitious club.
"(London Irish director of rugby) Brian Smith's got a great eye for players, particularly in the southern hemisphere. I'm pretty excited about the squad he's building for next season."