Johnson has not featured in the Leeds side since the home defeat against Burnley, when he was on the bench.
"A few of my friends said I am lacking ambition joining a lower club," Johnson told Doncaster's website.
"But I know that this club is ambitious and I can get regular football - especially as my contract at Leeds is up in the summer."
His loan spell with the League One side takes him up to January 4 and he could make his debut for Rovers against Bristol City tomorrow evening.