Midfielder Green, 18, travelled with the first-team squad on their pre-season trip to Spain last summer and made his senior debut against Sheffield United in the home Johnstone’s Paint Trophy tie in October.
Smith, 17, who can operate on the wing or up front, made his first appearance as a late substitute in the same match and made his full debut at Bury in February.
He has been a regular in Ronnie Moore’s match-day squad since and has made nine appearances in total.
“They’re both good players and, importantly, they both have fantastic attitudes,” Moore told the club’s official website.
“We’ve told them that they’ve worked hard to earn the reward of a professional contract but now they have to work even harder to continue their development with the first team.
“They’re both exciting prospects, there’s no doubt about that, and if they keep on listening to the advice they’re given then we’re confident they can become important players for this club.”