The 44-year-old former Barca player, who managed the club's B team between 2008 and 2011, left his role as Celta Vigo boss last week.
Barcelona parted company with manager Gerardo Martino after finishing second to Atletico Madrid in La Liga.
Sporting director Andoni Zubizarreta recommended Enrique, who has also managed Roma, to replace the Argentine.
Martino succeeded Tito Vilanova, who has since died of throat cancer, last summer, but his two-year deal was ended by mutual consent.
The 51-year-old was unable to prevent the club from losing the La Liga title for only the second time in six years as they drew with champions Atletico Madrid on the final day, in a game where a win would have clinched them the title.
Enrique's arrival had been widely expected because of his strong links with the club and a successful spell as B team boss where he replaced Pep Guardiola and led them to promotion to the Spanish second division in 2010 with a record points haul.
He left the role to join Italian side Roma for a season but after a year at Celta, he returns to the Nou Camp for a third spell.
A versatile midfielder and attacker, Enrique made 300 appearances for Barca between 1996 and 2004 which included a two-year spell as captain.
After joining the Catalans from rivals Real Madrid on a free transfer, the Spaniard won two La Liga titles, two Spanish cups and the Uefa Cup.
The appointment comes on the same day as the signing of Borussia Monchengladbach goalkeeper Marc-Andre Ter Stegen and Lionel Messi signing a new deal.
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