The 24-year-old is now contracted at the club until the summer of 2021, following in the footsteps of Jacob Brown and Cauley Woodrow, who agreed extensions earlier on in the close season.
Barnsley remain in talks with influential defender Ethan Pinnock – whose current deal expires next June – regarding fresh terms.
Conway said: “We are pleased to see Cameron sign a new contract with us. It is a well-deserved reward for how well he played last season, which was further recognised with him being included in the EFL Team of the Season.
“This is part of our stated strategy, to develop young players and extend their deals for as long as possible. We have seen Jacob Brown, Cauley Woodrow and Mike Bähre recently further their stays as well, so now we hope to see more players do the same.”
McGeehan added: “Off the back of last season, I want to continue the momentum.
“We had a really good season, it was great for everyone at the club to enjoy that, so I wanted to commit my future and carry on the journey.”