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.
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.