The 20-year-old, a former Manchester United youth graduate, made 18 appearances during a loan spell at Rochdale last season. He has yet to feature at first-team level for the Clarets.
Dodgson’s arrival follows on from the addition of a left-sided defender on Thursday in Rotherham United’s Jamie McCart.
Speculation is continuing to surround the future of Reds captain Liam Kitching, with Coventry City pressing ahead in their bid to bring him to the Midlands after two failed bids.
Reports in Coventry suggest the Sky Blues are increasingly confident in their quest to sign him at the third time of asking. The fee being mooted is less than £5m.
Barnsley are remaining tight-lipped over the reports.
On bringing in Dodgson, Reds CEO Khaled El-Ahmad commented: “We are pleased to bring Owen to Oakwell.
“He is a young player who will continue his development while providing competition within our squad."
Dodgson said: “I’m very happy to be here. When the opportunity came about, I had to jump on the opportunity. I’m looking forward to the season.”
Barnsley are also hoping to bring in a forward before the deadline and have been linked with a move for Birmingham City’s Sam Cosgrove.