Detective Chief Inspector John Lehmann said the arrested man was known to police and had been the subject of intensive investigation.
"The evidence against him is quite comprehensive, which we'll be putting before the court," Mr Lehmann told reporters at police headquarters at Parramatta.
He said police would put physical, forensic and DNA evidence before the court as well as witness statements he labelled "very important to our brief of evidence".
Three years before Ms Wallace went missing, New Zealand nurse Marion Sanford disappeared from the same area.
Ms Sanford wrote a letter to her brother Peter in January 1980, saying she had gone to meet friends and would be back at the Cammeray home they shared within a week.
But the 23-year-old, who was working as a prostitute in Kings Cross to pay off her debts, vanished without a trace.
Detective Sergeant Robert George, who had been working on the case since 2008, earlier said her disappearances had been linked with Ms Wallace and another New Zealand woman Linda Davie.
At an inquest at Glebe Coroners Court in Sydney in 2012, he said the similarities were the geographical area where they all disappeared along with the ages and general description of the women.
Ms Davie, 22, was an aspiring model who had moved from New Zealand to live with her boyfriend in 1980.
About 10 weeks after Ms Sanford's disappearance, Ms Davie mailed a letter to her boyfriend saying she was going away for a few days.
She never returned home.
Today, Mr Lehman said Ms Wallace's friends and family were glad to hear an arrest had been made.
"They're very pleased with the result. They know it's just the start of a long court process," he said.
He called the arrest a "credit to the investigators who have put in tireless hours and an enormous amount of effort and dedication to this particular case".
