The utility player, who can play anywhere in defence or midfield, was not offered a new deal at Prenton Park and has now agreed terms with The Tigers.
Hinds becomes Hull's third signing of the summer, after they secured the signatures of Danny Allsopp and Andy Dawson.
"The deal with Richard is as good as done and I'm delighted. He's someone I first tried to sign when I was in charge at Leicester," Hull manager Peter Taylor told the Hull Daily Mail.
"He's a very, very good player although things didn't quite work out for him at Tranmere last season. We've managed to get him on low wages and the initial deal is for 12 months.
"However, there's a chance that could be extended. I think Richard wants to show Tranmere exactly what he can do and if he performs to anything like his ability, he will be an outstanding signing."
Hull are still looking to bolster their squad and look set to pursue their interest for Tranmere's Jason Price and Alton Thelwell of Tottenham.
