The striker, who saw a loan spell to Oakwell fall through in August, will link up with a Tykes side which sits 19th in the second tier – one point above the relegation zone.
McBurnie said: “I had a good conversation with the manager (Carlos Carvalhal) and we both agreed that I needed game time. With the options limited here, Barnsley was the perfect club for me to do just that," said McBurnie.
“It's taken me five months to get there after the move fell down at the last minute when I went there to sign at the end of August, but at least all the signing photos have already been done!
“It was disappointing to miss out in August, but I've had no regrets over the last five months. I've made my full Premier League debut and been involved quite a lot in the matchday squads, which I've loved.
“But now is the right time for me to try and play week in week out."
Meanwhile, Swans Under-23s goalkeeper Lewis Thomas has joined Welsh Premier League side Carmarthen Town on loan until the end of the season.