Attack-minded Leahy, 28, has been a chief target for boss Steve Cotterill and has completed his move to Montgomery Waters Meadow as a free agent, becoming the club's first new signing of a busy summer ahead.
Captain Leahy turned down the offer of a new contract at Bristol Rovers, relegated from League One after finishing bottom, in favour of staying in the third tier with Salop, who have monitored the former Walsall man for some time.
Leahy's two-year deal come's with a year extension in the clubs' favour after Cotterill's scouts watched Leahy extensively.
The Coventry-born defender, who has been relegated from League One with his previous two clubs, is Town's first new signing of the summer as Shrews boss Cotterill undergoes a rebuild of his squad having released 13 players.
Cotterill admits Leahy's eye for goals and assists are 'incredible'. The left-back scored 10 goals – including five penalties – last season for the struggling Gas, an impressive goal haul which included the opening in a 2-1 win against Cotterill's men in February. His contract expired this summer.
His 10-goal haul was more than top scorer Shaun Whalley (nine) managed for Town this season. He also registered five assists from the left-back role. The defender can also operate at left wing-back.
Cotterill said: "First and foremost, he scores goals and gets assists. He scored 10 goals last season from left-back. He's a great lad and a very fit boy. He has an eye for a goal and his assists are incredible really.
"He is a player I've had my eye on for a while – myself and our scouts have looked at him extensively. We are looking forward to welcoming him to the group of players that we have here."
Rovers chief Joey Barton insisted the club must fight 'tooth and nail' to keep hold of the player this summer. But Gas fans have said they can't blame the full-back for wanting to remain in League One following their side's poor campaign.
Leahy was a Town target under former boss Sam Ricketts and could have made the switch to Shropshire earlier last season having found himself out of favour at The Memorial Stadium. But he went on to make 44 appearances last term.
He will provide competition to Town starlet Nathanael Ogbeta, who made the left wing-back role his own after arriving from Manchester City in January and landed the young player of the season award.
Leahy joined Bristol Rovers from Walsall in 2019, having also been relegated from League One with the Saddlers. Prior to that he made more than 100 league appearances for Scottish outfit Falkirk.