The hard-running prop/second-row, 23, has joined subject to passing a medical.
He will return to the UK next week after asking for a release from his Brisbane deal.
England coach Wayne Bennett recruited New-Zealand born Savelio for Broncos from Warrington Wolves in 2017.
However, he ruptured an anterior cruciate ligament injury in his first pre-season game last year and saw his hopes of featuring in the NRL wiped out.
Savelio had a spell on loan with Castleford Tigers three years ago and initially came to England as a young child when his dad Lokeni signed for Salford in 1997.
He said: “I’m really excited for this new challenge, coming back to a competition I know well and getting back on my feet again.
“I’m looking forward to finding that love for the sport once more.
“Hull are a big club so I’m really grateful for the chance. The plans Lee Radford laid out on the phone sounded like they suited me perfectly.”
Hull had not made any major recruits in the off-season; Savelio’s unexpected availability is just the sort of opportunity they were holding out for.
Radford added: “Andre is someone in our recruitment meetings we’ve identified for some time and kept tabs on.
“We had initially looked at him for 2020, so to bring him over early is a great opportunity for both him and us.
“I’ve been a fan of his for a long time now and can see him being a great long-term accusation as an edge back-rower.
“We’re in a position where we have retained a lot of quality in our squad and added some fantastic new additions, coupled with the impressive contribution Gareth Ellis has made since coming out of retirement.”