The 24-year-old had been a free agent since the end of last season when he was released by Queens Park Rangers.
"I am really pleased to bring Angelo to the club, he is a talented player with a good pedigree," Rovers manager Darrell Clarke told the club's official website.
"He can play as a left winger or a striker, and will offer us some creativity in the final third. He is a player who can unlock defences and help us create the goals we have been lacking."
Balanta had five loan spells during his time at Loftus Road.