The 22-year-old, who was a former England youth international, started his career at Everton before joining Burnley in 2015.
Long had loan spells at both Fleetwood Town and Bolton Wanderers in League One last season.
"He is a quality striker and possesses real pace which frightens defenders," said Town manager Justin Edinburgh.
"I think all we will be adding now is another goalkeeper, which should complete a strong summer of recruitment for us. We are happy with the balance of the squad."
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League One club Northampton Town have signed Burnley striker Chris Long on a season-long loan deal.