The Premier League club announced on Wednesday that the Spaniard succeeds the long-serving Arsene Wenger.
Emery, who joined PSG in June 2016, left the French club at the end of this season, having led them to a domestic treble.
The 46-year-old had previously guided Spanish side Sevilla to three Europa League titles.
“Unai has an outstanding track record of success throughout his career,” Arsenal chief executive Ivan Gazidis said in a statement.
“He has also developed some of the best young talents in Europe and plays an exciting, progressive style of football that fits Arsenal perfectly.
“His hard work and passionate approach and his sense of value on and off the pitch make him the ideal person to take us forward.”
Wenger departed the North London club at the end of last season after nearly 22 years at the helm, helping the team capture three Premier League titles and seven FA Cups.