The news means the WBO belt would not be on the line if IBF heavyweight champion Anthony Joshua of Britain and Wladimir Klitschko agree to fight.
Joshua's promoter Eddie Hearn has said terms were almost agreed with former champion Klitschko and hoped the IBF, WBO and WBA titles would be contested.
But Ruiz Jr's promoter Bob Arum said the WBO has sanctioned the Parker bout.
The WBO is yet to confirm the decision but Arum is already considering venues and expects the match to take place in Parker's native New Zealand.
The 24-year-old is undefeated in 21 fights and is the WBO's number-one ranked heavyweight, with Ukrainian Klitschko second.
Mexico's Ruiz Jr, 27, is third on the list and has won all of his 29 bouts.
Fury has vacated the WBO and WBA straps and had his boxing licence stripped by the British Boxing Board of Control "pending further investigation into anti-doping and medical issues".
The 28-year-old, who defeated Klitschko in 2015, is suffering from depression and has admitted to taking cocaine. In November he also has an appeal hearing for a doping charge issued in July.
It is unclear if the WBA will allow Joshua to compete for their version of the title, but Hearn says his fighter will be in action on 10 December even if Klitschko pursues a fight for the belt with a different opponent.
On Thursday former British heavyweight champion David Price tweeted Joshua stating "I'm coming to knock you out on December 10".
Joseph Parker and Andy Ruiz Jr will fight for the WBO heavyweight title vacated by Tyson Fury on 10 December.