The World Cup winner and Arsenal footballer - who has co-founded gaming company Appnin Studios with friend, developer and digital artist Mike Friel - has launched the free title on iPhone and Android.
Ozil said: "I've always been passionate about computer and mobile games.
"Developing them has always been a dream, so setting up a mobile games studio when the time was right made perfect sense, and seeing your ideas evolve into games is very exciting."
This follows on from the first game he designed which was called 'Longest Kick', which was Apple's Game of the Day in over 100 countries.
The new game and its daily missions are designed to challenge, frustrate and excite players, and the Premier League star was keen to create something unique which could keep people entertaining during the coronavirus pandemic.
Similar to retro favourites in the 1980s, the new title - aimed at casual gamers - is distanced based, and features a character using a grapple hook to swing through a gauntlet of electrical reactors.
Diamonds can be obtained to unlock new characters and customise them with different 'grapplepacks', but players need to avoid falling into the never-ending river of acid.
Ozil added: "With 'Grapplepack' the most fun was creating the various characters and I even managed t sneak in one of my dogs, but you'll have to look very closely to find him."
'Grapplepack' is now available as a free download on the App Store and Google Play store.