Geldof said: "Playing again with the Rats and doing those great songs again will be exciting afresh.
"We were an amazing band and I just feel it's the right time to re-Rat, to go back to Boomtown for a visit.
"Also, I've always fancied playing the Isle of Wight Festival ever since I hitched there in the good/bad days when I was a kid.
"I saw The Who, Doors (I think), Hendrix and Leonard Cohen, who incidentally blew Hendrix off the stage, and Kris Kristofferson, who was also amazing -- God, so many cool bands.
"I also told several very boring frog anarchist types to go and f*** themselves and then stayed for a night in Hawkwind's tent.
"That's pretty IoW. Maybe Hawkwind are playing again this year. Maybe I could use the tent again. It will be a privilege to be on that stage, especially with a killer band like the Boomtown Rats."
Formed in 1975 in Dublin, the Boomtown Rats played their first UK shows with the Ramones and Talking Heads.
They were one of the biggest bands of the late 1970s into the 1980s with a string of top 10 hits and platinum albums, earning them Brits, Ivor Novellos and Grammys.
They became the first Irish band to have a UK number one with Rat Trap.
They will play on the main stage of the festival on Sunday June 16.