The midfielder made a popular impression as he appeared 22 times in a Rovers shirt during a four-and-a-half month spell on loan last season.
Rovers boss Darren Ferguson attempted to seal another move for the 21-year-old in the summer but failed as Grant signed a new deal with the Premier League club.
Instead, Grant went on loan to Championship side Ipswich Town but it was cut short due to limited game time.
Grant said: “I’m delighted to be back, it feels like I have unfinished business with Rovers after injury ended my loan spell last season and relegation.
“There were other offers, but the manager made it an easy choice for me. "The fans took to me last time, so it was a straightforward decision really.
“The manager told me how much he wanted me, and having a manager who has confidence and believes in you makes a real difference in football.”
Grant went straight into the squad to face Stevenage on Monday.