Unai Emery Etxegoien, a Spanish Basque, won the domestic treble with PSG this season.
And he became the surprise favorite to replace Arsène Wenger earlier this week after it had appeared former Arsenal captain Mikel Arteta about to take the job in the Emirates.
In his last year the club finished sixth in the Premier League, 37 points behind champions Manchester City and failed to qualify for the Champions League.
Arsenal will be wary of the turmoil at Manchester United after the departure of long-serving manager Alex Ferguson in 2013 but said the choice of Emery was unanimous.
"I am thrilled to be joining one of the great clubs in the game," Emery, 46, told Arsenal's website.
"Arsenal is known and loved throughout the world for its style of play, its commitment to young players, the fantastic stadium, the way the club is run. I'm very excited to be given the responsibility to start this important new chapter in Arsenal's history."
"Unai has an outstanding track record of success throughout his career, has developed some of the best young talent in Europe and plays an exciting, progressive style of football that fits Arsenal perfectly," chief executive Ivan Gazidis said.
"His hard-working and passionate approach and his sense of values on and off the pitch make him the ideal person to take us forward."
Emery left PSG this month after winning Ligue 1 and four domestic cups in two seasons in the French capital.