The pair, who are 19, both made their senior debuts for the club last season.
"Max and Tyrone have both done well this season and deserve their chance," manager Chris Wilder told the club's official website.
"They have worked at their game, listened to the right people and shown a lot of maturity. We are pleased that they will be part of the first-team squad next season."
Goalkeeper Crocombe made four appearances during the recent campaign, while striker Marsh spent part of the year on loan with Staines.