Scotland Yard said no further action was planned "at this time" against the man - believed to be a former bartender named John Gallagher.
Police flew out to New Zealand to interview Mr Gallagher after a new witness came forward with evidence about the 1992 killing of Ms Nickell in front of her two-year-old son, Alex, on Wimbledon Common, south London.
He was formally arrested and released on police bail until yesterday after returning to Britain and reporting to a police station last November.
A Scotland Yard spokeswoman said yesterday: "A 31-year-old man answered bail in connection with the Nickell inquiry today. The man is no longer on police bail, bail has been discontinued and there will be no further action at this time.
"A report has been submitted to the Crown Prosecution Service. They have been fully informed about our inquiries and we are working in close liaison with the CPS."
Police refused to confirm the man involved was Mr Gallagher.
But the inquiry, reopened after Colin Stagg was acquitted of the murder at the Old Bailey in 1993, is set to continue.
Ms Nickell, 23, died in a frenzied and apparently motiveless knife attack. Mr Gallagher, originally from the Roehampton estate near the common, emigrated to New Zealand shortly after the murder. He was later said to have been expelled for failing to disclose criminal convictions to authorities in Wellington.
Police started inquiries into Mr Gallagher after a former neighbour reported seeing a man with a heavily blood-stained shirt on the estate on the day of the murder.Reuse content