The 19-year-old will remain with the club until the summer of 2020.
Longbottom has made one appearance for Rovers this season, coming in the Checkatrade Trophy.
He has made nine appearances in total, scoring once.
“I’m delighted to have signed a new contract with the club, it has been a frustrating season for me as I have had a few injuries, but I am looking forward to making a few more appearances,” Longbottom told the club’s official website.“There are a lot of Development games coming up, so I am hoping to play in those games and after those I will speak to the gaffer and see what he says about the rest of the season.“Darren Ferguson is a fantastic manager, I have learnt a lot from him so far, he comes in everyday and gives you advice, he is a manager that gives you a chance no matter what age you are.”
Goalkeeper Ross Etheridge has had his contract with the club cancelled by mutual consent.
Etheridge had been transfer-listed by Darren Ferguson last summer after falling down the pecking order.
But a broken foot prevented the 23-year-old from earning a move away.
Rovers have also confirmed that the details of midfielder Tony Donaldson’s departure from the club have been finalised.