Leitch-Smith, 26, the Valiants' top scorer in 2015-16 with 12 goals in 43 games, rejected a contract offer.
Northern Ireland international McGivern, also 26, was released by Vale, having played 32 times last term.
In addition, Swiss goalkeeper Jayson Leutwiler, 27, has signed a new two-year deal with the Shropshire side.
Leutwiler has played 90 times during his two years at Shrewsbury, who finished 20th in League One after being promoted from the fourth tier in 2014-15.
"The environment and everything to do with Shrewsbury is very important to me," he said. "That was a massive factor in me re-signing here."
Shrewsbury boss Micky Mellon has now signed three Port Vale players in little over a week, following the arrival of Louis Dodds.
Leitch-Smith, who came through Crewe's youth system, joins up again with another former Alex Academy product, defender Matt Tootle, who missed over half of last season, having been sidelined by an Achilles injury.
"The manager is very ambitious," said Leitch-Smith. "And so are the type of players he is bringing in at the minute."
Mellon has now made six summer signings, having also brought in Fleetwood winger Antoni Sarcevic, Southend midfielder Gary Deegan. and Rochdale defender Oliver Lancashire.
Find all the latest football transfers on our dedicated page.
Shrewsbury Town have signed defender Ryan McGivern and striker AJ Leitch-Smith, whose contracts are due to expire at League One rivals Port Vale.