Ospina, 30, joined Napoli on a loan deal at the start of the 2018-19 season after finding his first-team opportunities with the Gunners further limited by the arrival of Bernd Leno.
And after making 24 appearances for the Italians in his first campaign Ospina, who represented his nation in this summer's Copa America before being eliminated by Chile in the quarter-finals, will remain at San Paolo in a transfer reportedly worth £5 million ($6.3m).
"Goalkeeper David Ospina has joined Napoli on a permanent transfer, following a season on loan at the Serie A side," a statement published on Arsenal's official website revealed.
"David joined us from Nice in 2014 after six seasons in Ligue 1, and made 70 appearances during his time with us. He was our goalkeeper in the 2017 Emirates FA Cup final win over Chelsea, and was also in the squad for the 2015 FA Cup final victory over Aston Villa.
"With 98 international appearances, David is the most capped goalkeeper in Colombia’s history and also represented his country at two World Cups – in 2014 and 2018.
Good luck, @D_Ospina1— Arsenal FC (@Arsenal) 4 de julio de 2019
"We would like to thank David for his contribution to the club and everyone at Arsenal wishes him the best for his future."
Ospina played the role of understudy to Petr Cech for most of his time at the Emirates Stadium, and was restricted to fewer than 10 Premier League appearances for each of his final three seasons before swapping north London for Naples.
With Cech also stepping down at the end of last season, Leno is expected to be deputised by Argentine shot-stopper Emiliano Martinez in 2019-20.
Martinez, who helped Reading avoid relegation to League One during his own loan spell in 2018-19, is determined to stay at Arsenal, despite playing just 14 senior games in eight years with the Gunners.
“My dream is to play for Arsenal. But it’s time for me to make it there or go somewhere else," he told Goal in April.
“I want to stay in England. My wife and my kid were born here and I want to stay at Arsenal - that’s the truth, so I hope they give me the chance.”