Midfielder Lewis Hall and defender Jack Batten, both 17, have been handed the deals after their recent progress at Under-18 and Under-21 level.
Willie McStay, Head of Academy Coaching, told the club's official website: "We're delighted to reward both Lewis and Jack with their first professional contracts.
"Both players have been captains for us and have excelled at Under-21 level. We've put together a group that are working hard together and we want to continue adding to that group for the benefit of the football club."
Luke Dobie and Kevin Krans, members of City's development squad, recently penned 18-month deals, while scholarship terms have been signed by youngsters Joe Morrell and Connor Lemonheigh-Evans.