The centre-forward, born to Ghanaian parents but of UK citizenship, has put pen to paper on a deal that keeps him at Turf Moor for 12 more months.
"Striker Daniel Agyei has signed a new contract to extend his stay at Turf Moor," the club announced via their official website.
"Agyei, who made his Premier League debut and a total of three substitute appearances for the Clarets at the end of last season, will be back in the fold for pre-season as the former AFC Wimbledon youngster looks to make a further mark at Turf Moor.
"Agyei has agreed a 12-month contract after returning to Burnley following two spells out on loan in League One this season."
Agyei made three Premier League appearances for Burnley in 2016-17 before being sent on loan this campaign.
"I'm delighted to be staying," said, the youngster.
"Hopefully I can come back next season and kick on and try and push for a place in the team."
Local reports say Agyei was among players visited by Ghana coach James Kwesi Appiah during his recent work trip to the UK.