The 18-year-old midfielder has signed a two-year deal with the option of a further year following a successful trial during pre-season.
He said: “I’m absolutely buzzing. I’ve been on trial since the start of pre-season, five weeks, and I’ve really enjoyed the games.
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“It’s a great bunch of lads and they welcomed me in really nicely. Steve (Eyre, assistant manager) and the gaffer have been excellent - all round lovely people.
“I couldn’t be more pleased.”
Degruchy joined the Minstermen aged 10 and progressed through the club's youth academy before signing his first senior contract last year.
He was released at the end of last term without making a senior appearance, but has featured for Rovers throughout pre-season.
Doncaster boss Gary McSheffrey said: “First and foremost he’s a great kid with a great attitude.
“He wants to be a footballer and he’s done everything in a five or six week period to do that.
“He’s trained every day. He’s been involved in every game and played in a couple of games with the youth team when we’ve asked him to. He’s just got on with things.”
Ex-Doncaster defender Tim Ryan is now youth team manager at York City and helped arrange a trial for Degruchy.
The youngster will be a development player at Rovers rather than a first-team regular, McSheffrey told The Free Press.
He added: “He’s integrated himself into the group really well and I think he’s a good prospect.
“He’s grasped the opportunity and we’re delighted to have him on board.”