Jayawardene is the sixth coach to have his appointment confirmed for the tournament for a men's team. The two men's sides yet to have their head coaches announced are the Oval Invincibles and Trent Rockets, with Tom Moody and Stephen Fleming expected to fulfil the respective roles.
That means than none of the men's sides will be coached by Englishmen, which Andrew Strauss, who stepped down as England's director of men's cricket last year, has labelled a "great opportunity" missed.
"Personally I think that [The Hundred] was a great opportunity for English coaches to be appointed," Strauss said. "Each of those teams will have their own reasons for appointing experienced coaches, who have coached in T20 cricket elsewhere in the world.
"You can completely understand that, but there is a bit of a chicken-and-egg situation in that unless English coaches get an opportunity, how do they get the experience?"
Jayawardene, who has coached Mumbai Indians to two of the last three IPL titles, will work alongside another member of their staff in Shane Bond. Bond is bowling coach at Mumbai Indians, and head coach at Sydney Thunder, and will be an assistant coach in The Hundred.
The job is first head coach role for Edwards, who has spent the past two season as director of women's cricket at Hampshire. She has also worked as batting coach in the Big Bash for Adelaide Strikers, and said "it's the right time" to make the step up to head coach.
"I feel like I've learned a lot from coaching overseas and working with the Southern Vipers," she said. "It's my time to have a go and see what I can do.
"I think The Hundred is going to have a positive impact on the game at a grassroots level. I'm really looking forward to being there from the start and watching it all unfold. It's really exciting because I've been to Australia and seen the impact the Big Bash has had and you just feel like we can do exactly that and more."
Jayawardene said that the tournament would be "innovative and exciting" and that it was a "great privilege to be head coach of the Southampton-based team.
"I think The Hundred will interest the world's best players because England is a great place to play cricket," he said. "The structure of the tournament is good and that means most of the guys will put their name in the hat because this is a tournament that excites them."
Mark Nicholas has been appointed as the franchise's chairman.