The 27-year-old has signed a two-year deal with the recently-promoted Tigers, with the club holding the option of a further year.
Moncur - who has become the club’s first addition of the close season - has previously worked alongside Tigers head coach Grant McCann during a loan spell at Peterborough United in the first half of the 2016-17 season.
That arrived shortly after Moncur joined Barnsley in a £500,000 deal from Colchester United in the summer of 2016, with the play-maker featuring twice for the Reds at the start of the 2016-17 campaign following the promotion to the Championship before leaving for Posh to boost his game-time levels.
Moncur returned to Oakwell early in the New Year in 2017 and featured 38 times in the following season.
The Swindon-born player, son of former West Ham schemer John, featured 27 times in all competitions in the first half of the Reds’ 2018-19 League One promotion campaign, but left for Luton in January 2019.
On signing Moncur, McCann said: “We’re delighted to have brought George to the club. There was a lot of competition for his signature and I worked with him for a brief period at Peterborough.
“George is a bubbly character and his nature and attitude will fit into our group, and he will complement the attacking players in our team.
“He’s very attack-minded and travels with the ball at speed. He can play in any of the front three positions or as a 10, and loves to take the ball off his back foot and get at people.
“He knows what it takes to win having achieved promotions in his career and he was part of a successful Luton team last year in the Championship.”