The 19-year-old striker made his Oxford United debut in December 2020, with his breakthrough campaign coming during the 2022/23 season.
He played 35 times that campaign, 25 as a substitute, and scored twice.
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O’Donkor made 26 appearances last season, with all but three from the bench, before joining Vanarama National League side Barnet on loan in February.
He enjoyed a productive temporary spell with the Bees, netting six goals in 14 matches.
O’Donkor has made two substitute appearances for the U’s this season, and links up with a Pirates side sitting 14th in the third tier.
United head coach Des Buckingham said: “With Gats, we put him out on loan last year and he went to Barnet, and did extremely well.
“He came back, and you see the impact that’s had on his development. He came back in and played in pre-season for that reason.
“To be able to secure him a move to a very good team in League One, in Bristol Rovers, shows with us being promoted, we’re able to loan our players to good clubs in the league below. That’ll be a wonderful move for him.”
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O’Donkor told the Pirates website: “It feels amazing to be a Bristol Rovers player. I can’t wait to get out there and show people what I can do.
“Speaking with the manager, I feel the way he wants to play really suits me. I just can’t wait to get out there.
“Bristol Rovers has always been a tough place to go. Obviously, the way the fans are, they’re always backing the team. They make it a tough place to go for teams, so I can’t wait to be a part of that.
“I just want to give 100 per cent every game and score as many goals as I can. Promotion is the end goal for every team in the league, so we’ll see how that goes.”