Jackson and Beau-James Wells will join older brother Byron in the New Zealand team at next month's Winter Olympics in PyeongChang.
New Zealand Olympic Team freeskier Byron Wells
Source: Associated Press
Their selection comes just three days after injury forced oldest brother Jossi to withdraw.
The 27-year-old was provisionally selected after tearing his patella tendon last June, but pulled out after training on snow showed his knee wasn't ready for the loading required to compete at Olympic level.
Jackson, 19, will compete in freeski slopestyle and 22-year-old Beau-James in freeski halfpipe.
PyeongChang will be Beau-James's second Winter Olympics following his sixth placing in halfpipe at Sochi in 2014.
"It's sad that Jossi will not be coming with us, but I'm really excited that two of my brothers will be there with me," he said.
Jackson is looking forward to following in his brothers' footsteps at his first Olympic Winter Games.
"It's a huge shame Jossi won't be there to compete with us because he's the one who first gave a profile to New Zealand freeskiing."
Jackson had a minor operation last week to get a piece of cartilage taken out of his right knee, but says his recovery is progressing well and he expects to join Byron and Beau-James at the X Games in Aspen, Colorado on January 25.
The New Zealand team now stands at 12, with further additions still possible in freeski, snowboard, speed skating, skeleton and alpine skiing before the Game start on February 9.