Coutts, a member of the United squad that won League One with 100 points and then went up again to the Premier League shortly after, was released by Fleetwood Town at the end of last season and will link up again with Barton on July 1.
The Scot was a popular player at Bramall Lane, and could have played a part in the Premier League but for a broken leg at Burton Albion that stunted his progress and saw Oliver Norwood signed to take his place.
Rovers were relegated to League Two last season, finishing bottom of the table, and Coutts said: “I'm delighted to get it done early.
The staggering amount Sheffield United earned from Premier League last season compared to Leeds United, Newcastle United and Arsenal
“Linking up with Joey again was a big attraction and I can't wait to get going.
“He's just driven for success, he won't settle for anything less and has big plans for the season, to get out of the league and get straight back up.
“So we're looking forward to it and hopefully I can help out.”
“It'd be nice to add another promotion,” Coutts added.
“I got a taste for League Two last season with Salford and it's going to be a tough division but one we should be fully capable of getting out of at the first time of asking.
“It's a tough division, and particularly difficult with no fans and atmosphere in grounds. It'll be brilliant to get fans back and hopefully we can get off to a good start.”
As well as Coutts, Barton has also signed Sam Finley, Mark Hughes and Nick Anderton.
“They are all lads that have predominantly played for northern clubs,” Barton said.
“So to attract them down south, it had to be a project that really excites them.
“We have been speaking to them about the ambition of the football club and the direction we want to move in.
“We want people that aren’t going to be freaked out by some of the away grounds in the division and that have been promoted out of the league and have been part of title-winning sides.”