The 18-year-old goalkeeper is tipped for a big future and he featured on the bench for Oldham last season.
Everton have now moved for the youngster and he has put pen to paper on a three-year deal at Goodison Park.
“I’m really excited for the challenge,” Renshaw told Everton’s official website.
“I know about the record of how many players Everton have brought through the Academy. That interested me a lot because there seems to be a serious pathway to the first team.
“Every time we played friendlies at Everton, I always used to say the training ground and facilities would make this an amazing club to be at.”