McBurnie, 19, who made only four senior starts for Bradford, has put pen to paper on a three-year deal and will join the Swans' development squad.
"I'm really excited about getting started," McBurnie told Swansea's official website.
"I've known about the interest for a little while now but it all got finalised pretty quickly and the hard work starts now.
"I'm thankful for everything that Bradford has done for me, but when a club like Swansea comes in for you then you can't say no.
"It's the perfect opportunity for me and the right time to sign
Hopefully I can have a good start for the Under-21s and continue to learn and develop during my time here.
"Swansea are now playing Category One games and they are the best fixtures in the country
You want to challenge yourself against the best players and I'm really looking forward to getting started."
McBurnie made his debut for Bradford against Rotherham in the FA Cup in November 2013 and the first of only two league starts followed a month later against the same club.
He made a total of 20 appearances for the Bantams, 16 as a substitute, but failed to score and had two loan spells at Chester last season, scoring five goals in 14 games
Source : PA
Source: PA