The Colombian number one joins from Ligue 1 outfit Nice for £3 million.
Nice confirmed Ospina's move earlier on Saturday after losing their friendly with Brentford 3-2. Manager Claude Puel admitted that the goalkeeper had signed for the Londoners, though it would be Sunday morning before Arsenal would confirm the deal.
The Colombian was an impressive performer during his nation's march to the World Cup quarterfinals this summer, and at 25 will have plenty of chances to add to his 44 caps.
Arsene Wenger has confirmed that Ospina will initially be back up to regular number one Wojciech Szczesny upon his arrival, though admits he is more than capable of seizing the goalkeeping jersey for himself.
Upon announcing the goalkeeper's arrival, Wenger had this to say: "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 will now take the place of departed goalkeeping duo Lukas Fabianski, who moved to Swansea on a free transfer despite starring in the club's FA triumph in May, as well as Emiliano Viviano, who failed to make an impression during his year-long loan at the Emirates despite arriving from Palermo as an Italian international.