WRU chief executive Roger Lewis confirmed he had concluded a deal which would see Edwards remain as Wales defence coach for what is understood to be at least another four years.
The move, which is expected to be officially announced, ended any chance of former Great Britain rugby league star Edwards joining England's coaching team in the build-up to the 2015 World Cup.
Edwards had been a free agent since leaving his role as Wasps head coach this month, with his previous Wales contract expiring at the end of the World Cup last month.
The 45-year-old was heavily linked with a role with England, with Martin Johnson's future as manager in some doubt following the side's dismal showing on and off the field in New Zealand.
But if the crisis-ridden Rugby Football Union were thinking about appointing Edwards to any position on their coaching staff, they have missed out again, having also failed to prise him from Wales three-and-a-half-years ago.
Lewis told Walesonline: "It was more than apparent through the extraordinary coverage in the UK press that Shaun was in considerable demand from many quarters and there were many options open to him in this country and in Europe.
"He smartly went off to New York last week just to get out of the country, because he was quite literally being bombarded.
"I kept in touch with him daily out there and concluded matters positively on Saturday.
"I'm delighted for Welsh rugby, I'm delighted for the team of coaches we've got and I'm delighted for Shaun.
"He has proved himself as a coach at the very highest level and we know what huge respect and affection he is held in, not only by the players but also by the Welsh rugby public.
"Our whole focus must be building on that and looking to the future.
"That is why the appointment of Shaun Edwards is so important."
Edwards, who also looks set to work with Wales' age-grade teams, had suggested earlier this month that he might consider an approach from the RFU.
"You consider any roles when you're a free agent," he said at the time.
"I'm here if anyone makes me an offer."
Edwards will be free to take on a coaching role at a club side in much the same way as he did while in charge at Wasps, although it is unlikely to be on a full-time basis.
Cardiff Blues chairman Peter Thomas had expressed an interest in Edwards becoming his side's part-time defence coach, but the latter appears to favour a return to the Aviva Premiership.
Lewis added: "Shaun really gets switched on and motivated by weekly rugby and he wanted to keep a link with the English Premiership.
"He's currently in negotiation with an English club. He won't leave the Wales camp in Test week, but there will be an opportunity for him to keep his hand in with the Premiership."
Edwards has enjoyed huge success since moving into coaching in rugby union 10 years ago, despite having not played the code professionally.
He helped Wasps win four Premiership titles and two Heineken Cups during his decade at the club.
He succeeded Warren Gatland as head coach in 2005 and was reunited with his mentor in the Wales set-up in 2008, immediately helping the country score their second Grand Slam success in four years.
But his crowing glory was arguably his role in their run to last month's World Cup semi-final, which saw them go agonisingly close to a first ever final appearance.
Earlier this year, Edwards' job briefly appeared to be on the line when he was accused of headbutting the team's sports scientist, Fergus Connolly.
He admitted to a scuffle - which saw both men fined £500 and banned from Wales' final RSB 6 Nations match in France - but denied butting his colleague.