The 24-year-old, a free agent after his contract with Rovers came to an end, has agreed a two-year deal at Fratton Park.
Bennett told the club website: “This is a massive club with a great fan base and the manager expressed a desire to bring me here.
“I know he’s very attack-minded – which is good for players like me – so that also helped me make this decision.
“I’ve had a few other offers from the league above, but I certainly don’t see this as a backward step.
“This club are looking to go somewhere and I want to be a part of that. I know what it takes to win promotion from this division because I’ve done it before.”