The former Scotland Under-20 international, who has become a sought-after commodity following a raft of impressive performances, joins Gloucester after three seasons at Headingley.
"He's somebody who stands out at Championship level," coach Nigel Davies is quoted as saying by the club's official website. "Leeds are a good team, who play a particularly good brand of rugby and who are fighting hard to get into the Premiership.
"Steve's been a big part of their success. He's a very strong, very powerful runner from deep and who hits good lines. He was part of the Edinburgh Academy at one stage and moved to get more opportunities.
"As a result of playing in the Championship, he's gained a lot of experience and he's shown his quality. I'm very excited about this guy. We're bringing really explosive players into the back line, who have got a big physical presence and that's important."
Gloucester are currently ninth in the Aviva Premiership table.