The Colombia international has signed what Goal earlier this week revealed to be a four-year contract after a deal worth £3.5 million was agreed between the two clubs.
Ospina became one of the most coveted goalkeepers in Europe after a string of impressive performances at this summer's World Cup in Brazil, and will now compete with Wojciech Szczesny for the No.1 spot.
The 25-year-old will make his debut for Arsenal in the Emirates Cup pre-season tournament, which takes place on the first week of August.
Gunners boss Arsene Wenger told the club's official website: “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."
Ospina made 189 appearances during a six-year spell at Nice and has been capped 49 times by Colombia.