The 23-year-old, who scored 24 times in 73 appearances for the Shrews between January 2011 and June 2012, has returned to the club and signed a two-year deal with the option for another year.
"It is a fantastic signing for us and I'm sure that the return of Collo will please the Town fans," chief executive Matt Williams told the club's official website.
"James has been our number one target and a lot of time and effort from the chairman and manager has gone into this deal and we are delighted to have reached an agreement with Hibs to secure James for the next two years."
Collins scored six times in 27 starts for Hibs last season and could not help them avoid relegation from the Scottish Premiership.
The move is described by Hibs' new chief executive Leeann Dempster as 'a mutually beneficial deal' as they look to rebuild their squad.