SYDNEY, Australia — The 36-year-old cold case had always been memorable: Lynette Dawson, a nurse and child care worker, vanished from a coastal suburb of Sydney, leaving two young daughters behind. Days later, her husband, an athlete turned teacher, moved in with the couple’s 16-year-old babysitter.

She was his student, and they were having an affair.

These details and others are at the center of “Teacher’s Pet,” a podcast whose investigative journalism has catapulted it to 27 million downloads and the top of the charts for true crime.

Now, after almost four decades of speculation, there’s been a break in the case. The police have arrested Chris Dawson, 70, and on Thursday he was charged in Sydney with the homicide of his wife. It was an “important step forward” toward justice for the Dawson family, said Mick Fuller, the New South Wales police commissioner.

The criminal charge has vindicated the suspicions of those who believe that Mr. Dawson killed his wife in order to be with his girlfriend. Greg Simms, Mrs. Dawson’s brother, told The Australian the family was “completely over the moon” with the development.