The 20-year-old has been an integral part in the South Yorkshire side's climb to ninth in the League One table.
And he will stay at the Keepmoat Stadium, who the Iron will visit for the first-ever time this weekend, until the end of the season.
"It's good news for us and will benefit Jono with him being settled now," said Sean O'Driscoll, who quit his role as Bournemouth manager earlier in the season to replace Dave Penney as Rovers boss.
"He brings speed to the front and he his still learning his trade.“Hopefully when he goes back to United he will be a better player with the experience he gets with us."