McBurnie, who enjoyed his first full campaign as a professional with City last season, has signed a three-year deal with the Swans. He is now expected to link up with their Under 21 squad.
The 19 year-old leaves Phil Parkinson's squad after impressing towards the end of last season during a loan period with Chester F.C and during his time with Scotland's Under 19s in their UEFA European U19s Qualifying tournament back in March.
The tall forward also caught the eye in August 2013 when he finished as top scorer for Manchester United during the Milk Cup youth tournament in Ireland.
McBurnie continued his eye-catching form going into the 2013/2014 season by scoring a large number of goals for City's youth team.
With injuries affecting Phil Parkinson's squad at the time, McBurnie was fast-tracked into the first team squad for his senior debut at Rotherham United in the FA Cup in November 2013.
McBurnie was then handed his first start with Parkinson's side on Boxing Day against the same opponents.
Despite only turning nineteen last month, McBurnie made twenty appearances in total for City before securing his move to the top flight.
Having come through City's youth ranks, McBurnie's move to Swansea sees him join an increasing list of players to move onto Premiership clubs in recent years after first developing their talents as youngsters with the Bantams.
Speaking about McBurnie's departure, Parkinson said: "We recently received an offer for Ollie from Swansea which we decided to accept.
"It is a great opportunity for him as he is a player with great potential.
"Ollie burst onto the scene scoring a lot of goals for the youth team and we put him into the first team at the time because of injuries when physically he wasn't ready yet.
"It was tough for him during this period because he came virtually straight from Saturday morning youth football into competitive first team action.
"He naturally found the going tough but he was still able to show flashes of quality.
"That period did probably knock him back a bit and with him being a local boy, there was also a lot of expectancy on him.
"To his credit though, he went away on loan to Chester in the second half of last season and did really well. It certainly isn't easy for a player of his age to impress at conference level and score goals.
"Even though he is still physically developing, he was excellent for them.
"As well as his time with Chester, he has performed to a good standard for Scotland at Under 19 level in recent months. In the company of players playing for teams at higher levels, he has acquitted himself well for his national side.
"I am sure that has helped to alert Swansea to Ollie's potential. We certainly wish him all the very best."