The 24-year-old centre-back has joined the Bundesliga club on a five-year contract until 2031, with reports claiming the transfer fee is around €25 million.
Esteve leaves Turf Moor after two-and-a-half years with the Clarets, initially arriving on loan from Montpellier in January 2024 before making the move permanent.
He played a key role in Burnley’s promotion-winning Championship campaign, featuring in all 46 league matches as the club recorded one of the division’s best defensive records.
The former France youth international remained a regular in the Premier League last season, making 34 appearances, but could not prevent Burnley’s relegation.
He now begins a new chapter in Germany with RB Leipzig, while Burnley thanked him for his contribution and wished him success.