The French defender was attracting major transfer interest after a superb last season in Burnley's promotion-winning campaign.
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Esteve has now committed to a new deal to 2030 with the Clarets.
He told the club's website: “I’m very happy to sign another deal, to me this Club is so special.
“When I came here, straight away I thought it was special, my family felt it too. It’s the best decision to stay at Burnley, for my progression and to play in the Premier League.
"This Club - with the Gaffer, with my teammates - is the best place to be. I’m proud to sign a new deal.”