The 22-year-old joined Plymouth Argyle on loan in June, but an ankle injury saw the youngster return to Molineux without making an appearance.
Now back to full fitness, the Wolves Academy product, who has made seven senior appearances for the club, recently played in the under-23s’ victory over West Brom.
His new club are competing in the Scottish Championship and Burgoyne could make his debut against Inverness on Saturday.