The 21-year-old joined Swansea in 2015 but had to wait until August of the following year for his first-team debut, going on to make five Premier League appearances for the club last season.
McBurnie has also been involved in each of Swansea's three Premier League games this term, but he will spend the remainder of the campaign in the Championship with Barnsley.
"Oli is a player that we targeted early this summer and have successfully brought to the club, which has not been a secret," manager Paul Heckingbottom told reporters.
"He is a Yorkshire lad and has jumped at the chance to come here on loan for the season. He will add some height and goal threat, along with that raw element of being an unknown quantity to Championship defences. I am looking forward to him coming into training and getting started."
McBurnie could make his debut for the club against Preston North End on September 9.