The Sheffield-born academy graduate has committed his future until the summer of 2022 with Rovers holding the option for a further year as part of the deal.
Greaves made his Rovers debut last season in the Leasing.com Trophy and followed up with his first league appearance for the club off the bench against Swindon Town this January.
Since then he has made a further six league appearances including three starts.
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Greaves follows Jon Taylor in signing a new Rovers deal this week.