Lenglet has been one of Sevilla's stand-out players this season, with then coach Vincenzo Montella admitting earlier this year his French defender had the talent to play for a club like Barcelona.
He is yet to be capped by France at senior level but has won 10 caps at Under-21 level.
He becomes the fifth centre-back in Barca's first-team squad, but Thomas Vermaelen, Samuel Umtiti and Yerry Mina have all been the subjects of transfer speculation.
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Lenglet, a former France under-21 global, becomes Barca's second signing of the summer following confirmation last week that Gremio midfielder Arthur Melo will also join the club this month. The Spanish champions have launched a second bid of £60m for Chelsea winger Willian.
But Ernesto Valverde has returned with an improved figure which is certain to test Chelsea's resolve as he looks to add an extra dimension to his attack this summer.
Lenglet played 35 of Sevilla's 38 La Liga matches in 2017/18 and was part of a defence that conceded 58 goals across the campaign, finishing seventh in the table.