The 31-year-old pleaded guilty to dealing methamphetamine and possessing heroin in January following his arrest in New York last year.
And in court he publically apologised to his "family and loved ones for putting them through this nightmare of my making".
In deciding Cameron's sentence, Federal Judge Richard Berman took into account more than two dozen letters written on his behalf, including a five page letter from his father and another from his mother.
In his message, Oscar-winner Michael said of former DJ Cameron: "I love my son, but I'm not blind to his actions. I don’t want to see him break.
"He is an adult and responsible for his own actions. We do know, however, that genes, family and peer pressure are a strong influence on a substance abuse."
Michael, 65 - wed to Diandra from 1977 to 2000 - also admitted he was largely absent during his son's upbringing, writing: "Cameron grew up in a bad marriage".
He then added: "I have some idea of the pressure of finding your own identity with a famous father. I'm not sure I comprehend it with two generations to deal with."
Cameron's grandfather Kirk Douglas and Catherine Zeta-Jones also sent hand-written notes, the actress describing her stepson as "a caring, considerate, worthy human being."
California-born Cameron, who has spent the last eight months in prison on remand, told the court he wanted to live a drug-free life.
"If I should be so fortunate as to have another chance, I will never squander that opportunity," he said.
Upon sentencing, the judge noted that Cameron had been a drug abuser since the age of 13, acknowledging that he had been clean since entering prison in August.
But he added his doubts that Cameron could walk away from drugs for good.
"That will be a very difficult chore," he told the court. "I think this case and this sentencing may well be his last chance to make it."