Republic of Ireland international midfielder Potter, 25, who spent five months on loan at Hillsborough from Wolves last season, has signed a three-year contract after the two clubs agreed an undisclosed fee.
Owls manager Laws said: "I've made the signing of Darren Potter one of my priorities this summer and I'm delighted to secure his signature.
"Darren impressed me enormously during his loan period last season and he'll now prove a very welcome addition to my squad on a permanent basis.
"As you would expect, securing the services of a player of Darren's calibre has taken longer to complete than some of our other signings and I'd like to place on record my thanks to the chairman, Lee Strafford, for the role he has played in supporting my efforts
to significantly strengthen our squad this summer."
Potter started his career at Anfield and made two Premier League and a Champions League appearance for Liverpool before loan spells at Southampton and then Wolves, for whom he signed permanently in January 2007. He arrived at Hillsborough on loan in January and made 17 appearances for the Owls.