The former London Wasps head coach has signed a new four-year contract to remain part of Warren Gatland's team.
Edwards had been linked with England but Williams is pleased he remains with Wales until the 2015 World Cup.
"It's a great relief for us as players to know that Shaun's going to be staying," he said.
"He's been very successful since he arrived."
Edwards joined head coach Gatland's backroom staff in 2008, the year in which Wales won the Grand Slam.
The 45-year-old's contract with Wales expired following the World Cup and he left his role with English Premiership club Wasps after 10 years.
"I think the World Cup has certainly shown defensively we are up there with one of the best in the world," added Williams.
"A lot of that is down to Shaun.
"I'm certainly very relieved that he's going to be there for a number of years and I'm sure the whole of Wales is."
Edwards has been part of a backroom team that has also included skills coach Rob Howley, forwards coach Robin McBryde and kicking coach Neil Jenkins.
Gatland and Edwards have committed their long-term futures to Wales and Williams hopes the coaching set-up will stay in place in the build-up to 2015 World Cup.
"Hopefully they can all sign pretty soon," said Williams. "We've got a great squad in Wales and that's not only the players.
"The coaching staff, the likes of Rob, Warren and Shaun, work very well with each other.
"They do work well off each other and that's great to have. It's pretty much like a rugby team really.Edwards has made a big impact - Warburton
"You can have all the superstars you want, but if they don't work well with each other and don't get on with each other it's not going to work.
"I think that's why Rob, Gats and Shaun work well off each. They have worked with each other before and they're mates as well."
While Edwards has committed himself to Wales, Williams will bow out of the international scene next month.
Head coach Gatland has confirmed the 34-year-old will start against Australia on 3 December in Cardiff.
The Ospreys player had already said the clash against the Wallabies will be his final appearance for the national side.
"I hope I remain fit up until then and I can play in that game or be involved in some capacity," said Williams.
"There's no better place for me to play than at home at the Millennium Stadium.
"I'll have all my friends and family there. It will be a great day for me and hopefully I can sign off in style."