The 20-year-old, who had been linked with City for some time, joined Spurs for £1m in 2007 from Leeds United.
City boss Keith Millen told BBC Radio Bristol it is a signing which should give him more options in midfield.
"He's one we feel would enhance the squad in terms of the position he plays and we've been looking for a left-sider for a while now," Millen said.
The deal is until the end of the current campaign, but Spurs do have the right to recall him after the opening 28 days of the agreement.
Rose is unavailable for City's trip to Scunthorpe on Saturday because of a slight ankle injury, picked up playing for the England Under-21s, but is expected to be fit for their home game with Watford.
Meanwhile, City have confirmed that they have released Peter Styvar's contract with immediate effect.
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