The move brings to a close a nine-year stay in Bournemouth for Travers, after he joined the academy in July 2016. He has agreed a four-year contract with the Toffees, who will open their new stadium at the start of the forthcoming season in an exciting new era for the club.
The Republic of Ireland international told club media how happy he is to make the switch as he takes a leap of faith in his career.
"I'm extremely proud and excited to be an Everton player. Coming in, you can feel how big this club is and the history that comes with it. You really feel that with the fanbase, the new stadium now as well and the direction the Club is going in.
"It's a fresh start for me to come up here and try a new chapter in my career.
"It's a really exciting time to be part of this massive football club and I just can't wait to get going."
The 26-year-old will rival Everton goalkeeper Jordan Pickford for the spot between the posts. Travers hopes he can take Pickford’s place under manager David Moyes as he aims to learn everything he can from the England international.
"Jordan (Pickford) is an outstanding goalkeeper for Club and country. I'm looking forward to competing with everyone here and being a Premier League player.
"Being in this environment is huge. We're going to push each other every day in training and whatever happens on the weekend, we're going to be there for each other and make the most of every opportunity that comes.
"It's always really exciting to work with a new group and being able to help the younger lads as well. I'll give it everything. I'll take pride in doing the right things on and off the pitch and representing this club with a lot of pride."