The defender informed the club he was willing to accept terms on a one-year deal and was due to arrive at Cappielow this morning to finalise the move.
Evans, 21, has promised Ton fans they have yet to see the best of him and is excited by the chance to continue to improve under the tutelage of Cappielow boss Allan Moore.
Evans told the Tele: "I enjoyed working under him this year. For the first six months, I probably wasn't at my best as I was getting used to new surroundings and a new way of playing.
"I felt I did a bit better towards the end of the season, but I'm looking to push on and get even better next year.
"I don't think I showed what I can do, as I can do a lot better. I'm delighted to stay on to work under the manager.
"I'm also looking forward to working under his assistant Mark McNally, as he played in the same position I'm playing and it will be good to learn from him.
"It was great to be at Morton this season and to play a lot more games than I had been doing.
"It's a massive club, a sleeping giant as they say, and hopefully with a few additions we can push on.
"I've agreed to sign a deal which I'm really happy with. The manager has aspirations for next year and I'm delighted to be a part of that."
The defender, who can play at full-back and in central defence, becomes Moore's first new signing of the summer. And the Ton boss says he was impressed by the attitude shown by Evans during the year he spent on loan from New Douglas Park.
He said: "I have been really impressed by Grant's attitude this season. He has always come in and worked very hard.
"Grant is very much one for the future and he will continue to learn if he keeps his eyes and ears open."