Ospina, who brings to an end his six-year association with Nice, has agreed a long-term deal at the Emirates Stadium and will compete with Wojciech Szczesny for a starting berth, although manager Arsene Wenger has confirmed the Pole will start the season as the club's number one.
The 25-year-old was an integral part of the Colombia side that reached the quarter-finals in Brazil before being beaten by the hosts, with his displays bringing him to the attention of Wenger.
"David Ospina is an excellent goalkeeper, with good experience and a proven record of performing with Nice and Colombia," the Arsenal manager told the club's official website.
"He will add strength to our squad and we are very pleased that he will be joining us."
Ospina, who was embroiled in a Ligue 1 relegation battle last term as Nice finished just two points above the drop zone, joins defender Mathieu Debuchy and forward Alexis Sanchez in completing a close-season move to Arsenal.
Wenger's side will be looking to build on a promising campaign last time out as the club ended a nine-year trophy drought by securing the FA Cup and spent more than 100 days at the summit of the Premier League before finishing fourth.
Having started his career at Atletico Nacional in his homeland, Ospina moved to France to link with Nice in 2008, replacing current Tottenham keeper Hugo Lloris on the French south coast.
He subsequently made 189 Ligue 1 outings for the club and is one appearance shy of a half-century of caps for Colombia.
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