Rev David Hill and Sandra Hill said they were "blessed" to have had sons Jason, 31, and Stuart, 30, in their lives.
The brothers died alongside Stuart's girlfriend, 27-year-old Becky Dobson, in Saturday's crash at the Arizona tourist destination.
Three other British passengers along with the pilot survived - despite having to wait eight hours to be rescued.
The group had been celebrating Stuart Hill's birthday when the crash occurred.
Rev Hill and his wife said their sons would be "deeply missed by so many, many people".
In a statement they said: "We have a large extended family and Jason and Stuart were always at the heart of it, organising get-togethers and always with time for others.
"If ever either of us came home after a difficult day, Jason or Stuart would be there with a smile or a hug, and that was all we needed to lift our spirits again.
"We always did things as a family and as parents we feel blessed to have had them in our lives.
"Our sons were happy, outgoing people who loved cycling, walking and spending time with family and friends."
The statement added that the brothers shared an "incredible bond".
The circumstances of the crash are unknown.