Marino had a brief romance with the child's mother, Donna Savattere, when she was a 35-year-old production assistant at CBS Sports' Manhattan studio, the newspaper said.
At the time, the ex-Miami Dolphins quarterback was married to Claire, his wife of 20 years and mother of his six children.
The Post said Savattere gave birth to Marino's daughter, Chloe, in June 2005, after which Marino paid her millions of dollars to keep the child's parentage a secret.
"They had an affair, and she had a baby," a source told the Post. "Everything was on the down-low and secretive."
Marino, 51, confirmed the story to the newspaper, but said he did not intend to elaborate on it.
"This is a personal and private matter. I take full responsibility both personally and financially for my actions now as I did then," he told the Post in a written statement. "We mutually agreed to keep our arrangement private to protect all parties involved."
Marino said he and his spouse have no plans to split up.
"My wife and I have been married for almost 30 years and have six children together," he said in the statement. "And we continue to be a strong and loving family."
Marino is expected to help cover Super Bowl Sunday for CBS, the newspaper said.