The Frenchman's signing is likely to be made official on Wednesday after a medical. He will sign a five-year contract.
The Blaugrana paid Lenglet's full €35m release clause after failing to negotiate a lower fee for the 23-year-old.
Lenglet became one of Europe's most sought-after defenders at Sevilla, following his arrival from Ligue 1 side Nancy in January 2017.
Manchester United were also credited with an interest in securing his signature, but Lenglet has opted to stay in La Liga with Barca.
Sevilla made an effort to keep hold of Lenglet, but the defender rejected a new contract proposal from the Andalusian side.
Lenglet becomes Barcelona's second major signing of the summer, after Arthur arrived from Gremio for €40m on Monday.