The 39-year-old former NBA player discussed his drug addiction and its impact on his marriage to Kardashian during Tuesday's episode of Good Morning America.
Odom, who details his drug use in the new memoir Darkness to Light, voiced remorse at threatening to kill Kardashian.
"I'm pretty sure she had to be scared at that point in time. I'm thinking about it now, like, I couldn't believe how I was treating that queen like that," the star said.
"[I owe] her and her family an apology. Big time," he added.
Odom first started using drugs at age 12 and said he was "professional at hiding" his addiction from others. He said Kardashian didn't find out about his cocaine use and cheating for "a long time."
"You don't want your wife to know that you're sniffing coke and ... having sex with other women," the athlete said.
Kardashian split from Odom in 2013 after four years of marriage but supported Odom following his overdose and hospitalization in 2015. The pair finalized their divorce in December 2016.
Odom previously expressed regret in an interview with Us Weekly in 2017.
"If there is one thing I regret when I was married, it was having multiple affairs with different women. That wasn't the stand-up thing to do," he said.
Odom told Good Morning America said he "can't even remember" the last time he's done cocaine but said he smokes marijuana and occasionally drinks. Darkness to Light debuts Tuesday.