Moncur, 25, whose existing Oakwell contract was due to expire in the summer, has made just two league starts since the end of October with half of his 22 league appearances for the Reds having come from the bench so far in 2018-19.
As part of the deal, Barnsley have a future financial interest in the player, who joined the club in a Â£500,000 move from Colchester United in the summer of 2016.
The decision to sell Moncur follows the recent sale of Brad Potts to Preston North End earlier this month.
Chief executive Gauthier Ganaye said: “We have been in discussions with George’s representatives for a while, but it became very clear that he was not willing to sign a new contract.
"With six months remaining on his deal, it means you have to make a decision on his future. As well as that, he did not feature much over the course of the season, so this is a good deal for the club and the player.
“George wanted to increase his playing time and he moves back to the south of England, closer to his family. We wish him the very best of luck in the rest of his career, he has been a great character to have at the club.”
Moncur had been linked with a move to Portsmouth earlier in the January window.
Barnsley remain in the market for wide-sided midfielders to boost their options, with assistant head coach Andreas Winkler revealing that the club were close to a new addition in his press match press conference ahead of Saturday's game at AFC Wimbledon.