The 22-year-old, who came through the Lyon youth system, is at Euro 2016 with the France squad and, although yet to play, is expected to start the quarter-final against Iceland.
Barca president Josep Bartomeu confirmed the news on Thursday but did not disclose the length of the deal.
According to French media, Umtiti will sign a five-year contract.
Bartomeu also confirmed that Barca striker Neymar was close to signing a new contract despite reported interest from Manchester United and Paris St-Germain.
Barcelona have agreed to buy France international centre-back Samuel Umtiti from Lyon for about £21m (25m Euro).