The 19-year-old is becoming a fan favourite at Wetherby Road, making 28 appearances this season, scoring four goals in the process.
Kitching, who is on loan from Championship side Leeds United, scored the winner against York City in the FA Trophy earlier in the season.
Manager Simon Weaver expressed his delight at the club's capture and predicted a big future for the youngster.
“He did really well last season at centre half and has played well this year, at a higher level, in a position he’s not been accustomed to, so you’ve got to give him a lot of credit," he told the club's website.
“The modern centre half has to go out and defend in wide areas these days and playing on the left makes him more adept to that.
“I think he’s grown as well in terms of his size and he’s aggressive in the box with a nose for goals; he’s got a great future ahead of him.”