The 25-year-old starred at the World Cup with Colombia, helping his country to the quarter-finals in Brazil where they lost out to the hosts.
He made 189 Ligue 1 appearances during a six-year spell with Nice, where he was sent off on four occasions.
Ospina was a 17-year-old when he made his professional debut for Atletico Nacional in Colombia and he has won 44 caps for his country.
Arsenal are believed to have just over £3million for his services and boss Arsene Wenger said: "David Ospina is an excellent goalkeeper, with good experience and a proven record of performing with Nice and Colombia.
"He will add strength to our squad and we are very pleased that he will be joining us."
On Saturday night, Nice coach Claude Puel confirmed the deal and assured Arsenal fans they could expect some 'quality' from the new arrival.
He told Sky Sports News: "It's a good affair for Arsenal because he's a very good player. You will see next season the quality of this player.
"It's fantastic for him. It's important for him to try another league, another club and Arsenal is a fantastic club for him. You saw in the World Cup how important a goalkeeper he is."
Ospina tweeted to say: "On behalf of my family and myself, I want to thank you for the support. I want to share a neat story.
"Today is an important day in my career. A wonderful time ends with Nice, and a dream is fulfilled at Arsenal. Merci Nissarts, Go Gunners. Thanks for the support - you will forever remain in my heart."