Gallagher's High Flying Birds and the Scottish rock band will headline the event, which takes place in June next year.
Elbow, rapper and singer Example, The Vaccines, Noah & The Whale and Madness are also confirmed for the Main Stage, while The Christians top the bill on the Big Top Stage.
Madness said: "At last, we've been wanting to play the Isle of Wight Festival for ages now, the perfect way to start our summer."
It was recently reported that the festival planned to sign up more dance and urban acts, with Giddings hoping for an "American Trilogy".
The Isle of Wight Festival takes place on June 22-24 at Seaclose Park, Newport. Tickets, which are priced between £80 and £190, are on sale now. For more information visit www.isleofwightfestival.com.
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Watch the music video for Gallagher's new single 'If I Had A Gun' below: