The 25-year-old spent last season on loan at Aston Villa, helping the midlanders to the Championship play-off final, and returns to the second tier to join their local rivals.
Johnstone spent seven seasons at United, but never played a single minute for the Red Devils, instead being loaned out to a number of clubs, including Yeovil, Doncaster and Preston.
He played 45 times for Villa last season and is looking forward to returning to the Championship, having signed a four-year deal with the Baggies.
"I'm happy to be here. I've spoken to a lot of people about the club and heard nothing but good things," he told the club's official website .
"It's good to get through the door. I've played Championship games and won a promotion from League One with Preston but always seemed to end back at Manchester United or going somewhere else.
"Now it's time to settle down and take my game up to the next level which I believe I can do here."
West Brom boss Darren Moore believes the signing is indicative of what the club intend to achieve in the 2018-19 season, having finished rock bottom of the Premier League in 2017-18 .
Moore took charge of the Baggies in April following the departure of Alan Pardew and has been trusted to guide Albion back to the top flight at the first time of asking. He feels the addition of Johnstone is the first part of the process in getting West Brom back to the Premier League.
"Sam is young and determined to be the best keeper he can possibly be - he's hungry to do that with us at Albion," Moore said.
"We've had him targeted from the outset and we're all delighted to have him on board.
"He buys into exactly what we are trying to achieve and will hopefully represent the shape of things to come."