Andre Hanscombe said he was sorry he continued to believe that Mr Stagg had murdered the 23-year-old mother of his child on Wimbledon Common in 1992.
Mr Stagg spent 13 months in prison suspected of the crime before being freed by a judge.
Last year, 16 years after her death, Robert Napper, 42, finally admitted killing the former model in front of her two-year-old son in a frenzied knife attack.
Napper pleaded guilty to Miss Nickell’s manslaughter on the grounds of his diminished responsibility and was ordered to be detained in Broadmoor indefinitely.
In a letter, Mr Hanscombe, 46, who lives in France with the couple’s now 20-year-old son Alex, apologised to Mr Stagg.
It read: “I am sorry for the ordeal that you have endured during virtually the whole length of this very sad affair, and any part that I might have had personally to make it worse.
“I had been led to believe by officers of the Metropolitan Police that they considered you responsible for my partner’s death.
“I know now that you were, and are, an innocent man who was mistakenly charged. I wish you a long, happy and productive life.”
Mr Stagg was charged with murder in 1993 but acquitted in October 1994 when the case was thrown out at the Old Bailey.
Last year he won £706,000 compensation for wrongful arrest.
His solicitor Alex Tribick said he had seen Mr Hanscombe’s letter and his client was “very pleased”.
He said: “The apology was extremely welcome indeed, he was very pleased and very touched.”
Mr Stagg said: “It was a really kind gesture. I know how difficult it must have been for him to make.
“Understandably he spent years hating me. To him I was the man who destroyed the love of his life.
“After all those years it must have been very hard to come to terms with the proof that I was innocent. I accept his apology with gratitude. It means a lot to me.”
Last year, police apologised for their mistakes in not catching Napper sooner.
They apologised to relatives of Miss Nickell and Samantha and Jazmine Bissett, also killed by Napper, for missed opportunities to arrest Napper which could have saved their lives.
Officers also gave a public apology for the first time to Mr Stagg.
In November 1993, Napper savagely killed Miss Bissett, 27, and her daughter Jazmine, four, after climbing into their basement flat near his home in Plumstead, south-east London.
He was arrested in May 1994 and sent to Broadmoor for their manslaughter a year later.
Meanwhile, Mr Stagg faced a murder trial but the case was thrown out when police were criticised.
It was not until 2004 that new DNA techniques were able to match a speck of DNA found on Miss Nickell’s body to Napper.
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