The former Oasis rocker and his current group, Noel Gallagher's High Flying Birds are set to hit the road this summer, and will be supported at some gigs by Elijah's band Inhaler, including at a concert in the U2 frontman's native Dublin, Ireland, reports aceshowbiz.com.
Although Bono is his friend, but Gallagher says Elijah is joining his tour on merit.
"His (Bono's) son's got something. Eli has been getting it together for a few years now and has gone through the stages most young people do," the "Wonderwall" hitmaker told BBC Radio 2.
Gallagher: "He started off a bit like The Clash, a bit angry. They're good. They're going on tour with me in the summer. They're a bit like the Bunnymen and early U2. Which is a surprise."
Gallagher said that Bono thinks it won't be long until his offspring steps out of his shadow, adding: "Bono said to me the other night, 'The funny thing is that they've not realised yet that they're cool enough not to hang out with us.' I was like, 'I don't know what that means but it sounds profound'."
Gallagher's daughter Anais is an aspiring photographer and has created Inhaler's album artwork, and will also join her father on tour in Japan. However, he warned her not to expect an easy ride, adding there's "no such things as days off" as part of his entourage.
Inhaler feature Elijah on vocals and rhythm guitar, Robert Keating on bass, Ryan McMahon on drums, and Josh Jenkinson on lead guitar.
He formed the group with his friends while still at school and they released their debut single "It won't always be like this" in March.