Former Raith Rovers and Partick Thistle forward Nisbet, 23, moves to Easter Road on a four-year contract after scoring 23 goals in 32 appearances for the Pars last season.
Wright, 25, has agreed a two-year deal after leaving Saints, having spent several seasons with Colchester United before moving north in 2018.
Manager Jack Ross told the club website: "We’re delighted to have Kevin on board. It’s a position we wanted to strengthen. If you look at his profile, and where he is in his career, then I think it’s a really good fit for both parties.
"Drey was one we’d identified a long time ago, so we’re pleased. We’ve identified key areas in the squad where we think it’s important to strengthen and the wider area is one of them. We have Daryl Horgan and Martin Boyle but there’s not much width beyond that.”
Later on Friday, Hibs made their third new signing when midfielder Alex Gogic joined the Easter Road club from Hamilton Accies.