Burton, a left sided defender, and Peat, a defender/midfielder, have earned one-year pro contracts with the club.
Both got call-ups to the first team squad last year but didn't play. They have been influential players in the title-winning Juniors side, and also featured heavily for the Reserves over the last two seasons.
Meanwhile, City's Juniors lost 1-0 on Saturday in the Merit League. A late Hartlepool goal sealed the Monkey Hangers' victory, the third time they've beaten us this season.