Mikail Markhasev, a Ukrainian immigrant, was convicted in July, 1998, of murdering comedian Bill Cosby's 27-year-old son during a botched 1997 robbery. He was sentenced to life in prison a month later.
He sent a letter to authorities Friday confessing that he murdered Cosby in which he called his crime of four years ago an act of "great wickedness."
Los Angeles County authorities announced the development after Markhasev's lawyer notified the courts the appeal was being abandoned.
Kyle Brodie, a deputy attorney general acting for the state of California in the appeal case, released the contents of the letter in which Markhasev, 22, admitted his guilt.
"I am guilty and I want to do the right thing. More than anything, I want to apologize to the victim's family," the letter read. "It is my duty as a Christian and it's the least I can do after the great wickedness for which I'm responsible."
Markhasev also said that he wanted to abandon the appeal because "it's based on falsehood and deceit," Brodie said.
Markhasev added that he wanted to spare his family further public humiliation stemming from the ordeal. "It's not their fault that I'm here and as it is, I've already put them through hell," he wrote.
In his letter, Markhasev said he tried to get a message to the Cosby family about a month ago, but it did not suggest that he wanted to confess
CBS News Correspondent Chris Lawrence reports that prosecutors hope the letter brings some closure to Bill Cosby and his family.
"I think this moves them in that direction. And ultimately that's what is most important in this whole process," said Steve Cooley, the Los Angeles County District Attorney.
A spokesman for the Cosby family was not immediately available for comment.
Ennis Cosby, a graduate student at Columbia University, was home on vacation when he was shot to death while fixing a flat tire near a freeway off-ramp.
The Ukrainian-born Markhasev had been lurking in a nearby parking lot with friends shortly before he saw Cosby and decided to "jack" his car, Brodie said.
Prosecutors said during his trial that Markhasev was strung out on drugs at the time and looking for money to buy more.
In his appeal, Markhasev had asked for a new trial on the basis of allegations of jury and prosecutor misconduct.
Ennis Cosby was an educator who had been pursuing a doctoral degree at Columbia. He suffered from dyslexia had hoped to eventually open a school that offered alternative forms of teaching for children with dyslexia.
His death prompted a national outpouring of grief. It also spurred public outcry and partisan wrath over a move by Calif. Gov. Gray Davis, who was then the state's lieutenant governor, to offer a $50,000 reward in taxpayer money to help catch his killer.
At the time the Cosby familissued a statement refusing to accept taxpayer money. The Cosbys also established the "Hello Friend/Ennis Cosby Foundation," to sustain his work in opening doors for dyslexic people through early recognition, understanding and effective education.
Last October a documentary titled Ennis' Gift premiered. The film pays tribute to high-profile creative people with lifelong learning disabilities who found success despite the odds.
Brodie said he was "stunned" by the letter. "I don't know why he did this, is the short answer," Brodie said, adding that the appeal, filed in August 1998, was dismissed by the Second District Court of Appeal at noon on Friday after Markhasev and his lawyer abandoned a bid to overturn the conviction.
"He refers to his duty as a Christian. It's powerful, I think," Brodie said.
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