Martin Hibbert, 45, started the mission to climb Mount Kilimanjaro because he wanted to “move mountains” for people with disabilities.
He has already raised around half of the £1m donation target to fund the Spinal Injuries Association.
Mr Hibbert, from Chorley, and his daughter Eve, then 14, were six meters from suicide bomber Salman Abadi when he detonated his device five years ago last month.
Mr. Hibbert suffered a spinal cord severed by shrapnel during the attack which left 22 dead and hundreds injured.
He summitted Mount Kilimanjaro this weekend with the help of a personal team of assistants and local guides and porters.
They broke into song and dance after a grueling trek to the top of the 5,685m (18,652ft) high snow-capped peak in Tanzania.
Mr Hibbert said: ‘I could just see the sign at the top. I didn’t know if I should laugh, cry…it was such a relief to get there and know we made it. Something I will always remember. So proud.
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“I said we would all come back as different people and I definitely will, just love and that. I’m definitely a different person coming home and I think everyone else will be too.
“You know it doesn’t stop there, we’ve climbed a mountain but now we have to move mountains to get what we need in terms of social protection change, accessibility changes, things like that, so I’m going to need all these people to keep giving me this love and support.
“That’s why I’m doing this to show, don’t exclude someone because they’re in a wheelchair, look what they can do when they have the right help and support, they can climb Mt. Kilimanjaro.
“I hope this has highlighted how important help and support is.”
At the top, Martin spread some of his mother Janice’s ashes. She died in November last year and Martin said: ‘I said she was going to be with me. I love you mom.”
Nik Hartley, chief executive of the Spinal Injuries Association, told BBC Breakfast: “It’s important to understand there’s the physical feat of climbing a mountain.”