The 20 year-old has put pen to paper on a three year deal, which runs until the end of the 2019/20 season.
Peacock-Farrell has made one appearance for the first team to date, playing 90 minutes in the 1-1 draw with Queens Park Rangers, at Elland Road in April 2016.
The shot stopper featured regularly for the Under-23s during the last campaign and his performances were rewarded with a call up to the Northern Ireland Under-20s set up, for a training camp earlier this summer.