Etheridge, who is 6’5” tall, turned down the offer of a new contract with Accrington Stanley to join Rovers on a two-year deal.
Doncaster will have to pay compensation to Stanley for the 21-year-old.
Etheridge started last season at Accrington behind Jason Mooney but forced his way into the first team this year, helping the Lancashire club reach the League Two play-offs.
The former Derby County trainee also played a significant role in keeping Stalybridge Celtic in Conference North during a loan spell in 2014.
Speaking to the Free Press, Etheridge said: “I’m really pleased with the move. It’s a big club, great stadium, great crowd and a really good challenge for me.
“I’m expecting a challenge for the shirt but I’m coming here to give it my all and I’m very confident that I can do well.
“I’ve played a lot of games in non-league and I’ll get better the more games that I play at this level.
“I was gutted when I was released by Derby but my aim since then has been to climb back up the leagues and at Doncaster I’ve got the oppportunity to do just that.”
Rovers have transfer listed German goalkeeper Thorsten Stuckmann and have made no comment on the future of out of contract back-up goalkeeper Marko Marosi.