Rice, who captains the Owls' under-18s side, has agreed terms until 2021.
The youngster's progress was such that he was named on the bench for the senior team back in September for the draw with Yorkshire rivals Leeds.
Academy manager Steven Haslam said: 'He's a strong left-sided centre half, been in the system for a number of years and is the current captain of the Under-18s.
'This is a reward for his hard work but the challenge is there for him now to reach the next level and push on.
'He's been involved with the Under-23s, trained with the first team and been in a matchday squad.
'He's a level-headed player with high standards and we want to see him develop his career with us.'
Rice said: "It's a really proud day for me and my family. It's a dream come true."
Rice follows in the footsteps of fellow youngster Conor Grant after the midfielder also penned a senior contract earlier this month.