Mr Bowie will be extradited to Sydney on Saturday.
The 69-year-old has denied any involvement in his wife's disappearance and did so again when approached by A Current Affair.
"I didn't do it," he said.
Ms Bowie’s family said the news was a “very bittersweet moment” for them.
“There isn’t a day that goes by that I don’t think about mum and how kind, caring and loving she was,” her daughter Brenda Boyd said in a statement on behalf of the family.
“There are many things I miss about her, including her shy and sweet smile.”
Ms Boyd said she and her brother had never doubted how loved they were.
“She, too, was so loved by those who were lucky to meet her,” she said.
“I’m so thankful that police never forgot about mum and never gave up trying to find out why she was so cruelly taken away from us.”
Loading
Ms Boyd, who was six at the time her mother disappeared, told the inquest her mother was "most affectionate" and recalled baking cakes with her.
Mr Bowie also spoke at the inquest, and was open about his own behaviour including drinking and extramarital affairs.
He also admitted to forging his wife's signature on a land transfer document in 1984.
After his wife vanished, Mr Bowie told police they had argued and claimed his wife warned him that if he went to the pub, she would leave him.
Mr Bowie did go to the pub, he said, and when he got home his wife was gone, leaving behind their two children.
"I always struggled with that, I believed that she wouldn't have left us," Ms Boyd told A Current Affair after her father's arrest.
Ms Boyd said the family was coming to terms with the news of the arrest and requested privacy.
"Perhaps I'll get some answers - maybe not closure, but definitely more answers, and that will bring me closer to the truth of what happened last night," she said.
NSW Police have successfully applied for an extradition request and the man will be flown to Sydney on Saturday.
A million-dollar reward was posted for information, and in November 2018, a dam near Walgett was drained and searched.
Police used ground-penetrating radar to scan the concrete floor of a factory across the road from the Bowies' family home.
In March, the house was examined by scientific police using blood detection agents.
The next month, police combed a nearby paddock and found a silver ring with the letter R and other items.
Robbery and Serious Crime Squad Commander, Detective Superintendent Danny Doherty, praised the work of the investigators.
“We’ve had a dedicated team of detectives working on this investigation to uncover what happened to Roxlyn Bowie nearly four decades ago,” he said.
“The resolve of our investigators proves that we will continue to search for the truth – no matter how many years may pass.”
Anyone with information that may assist Strike Force Maluka investigators is urged to contact Crime Stoppers: 1800 333 000 or https://nsw.crimestoppers.com.au.
Esther Han is a journalist at The Sydney Morning Herald. She has covered state politics, health and consumer affairs.