"We're delighted both Tony and Mark have signed their new contracts," said Peace.
"The new deals are just reward for their efforts over the past 16 months.
"We believe Tony is one of the brightest managerial prospects around and we're really pleased to have secured his services for a further three-and-a-half years.
"It's been no surprise to us that Tony's name has been linked with jobs at a higher level.
"It's up to us to make sure we keep him focused and motivated, which we've moved to do by offering him this contract and giving him the platform to bring success here.
"The relationship between the chairman and manager is the most important in any football club and we enjoy a good one.
"Tony is a pleasure to work with and his brand of football has been a joy to watch.
"He has a great partnership with Mark, who has proved to be a key part of the team.
"We're all now focussing on trying to achieve our long-term goal of establishing this club in the Premiership."
Despite being linked to other management positions Mowbray expressed his delight at signing a new Hawthorns deal and building on the work already done since leaving Hibs and continuing the promotion push.
"I've enjoyed the challenge of the last 16 months of trying to get the club back to where we all feel it belongs," Mowbray said.
"We've got 15 big league games ahead of us now and it's important everyone connected with the club pulls together to achieve the same goal.
"The club has shown faith in what we're trying to achieve by offering us these deals and, with the continued backing of the board, we will strive to continually improve the football club."