The extension is worth $48 million and includes $30 million guaranteed, a source tells ESPN's Adam Schefter.
Hicks, 27, had a career-high seven sacks in 16 starts last season. He was entering the last year of his deal.
In talking to reporters in August, Hicks spoke confidently about his abilities on the field.
"I think you're always betting on yourself," Hicks said. "I think you're always saying to yourself, man, I'm going to do really good this year. I'm going to get a million sacks, I'm going to get a million tackles and I'm unstoppable. That's the way you approach every year and I think if you come back from that and you start putting restrictions on yourself then you're not going to get what you ultimately want."