The 17 year-old pacey starlet has put pen to paper on an initial one-month loan deal with City. Having trained with his new team-mates on Monday and Tuesday, Burke penned his loan contract in the club's southern hotel base ahead of the Swindon match.
Fresh from completing his loan move to the Bantams, Burke will now come into contention for the match at Swindon after receiving the relevant F.A and Football League clearances.
A product of the youth academy at the City Ground, the highly-rated wideman made his professional debut for Forest during their Capital One Cup tie against Tottenham Hotspur back in September.
Burke has since played in the Championship for Forest when he came on as a second half substitute in their entertaining 4-4 draw at Blackpool earlier this month.
The promising youngster will wear shirt number 24 during his time at City this season.
He has also been given permission by Forest to play in City's F.A Cup Quarter Final against Reading next month.
Speaking about the arrival of Burke, Parkinson said: "I just felt we needed a bit more pace in the side, and Oliver will give us that.
"He is young, but he's strong and can run with the ball.
"He is very highly fancied at Nottingham Forest and we are very much looking forward to working with him."