Lamar Odom is opening up for the first time about a crippling sex and drug addiction that nearly cost him his life.

In his new memoir, Darkness to Light — exclusively excerpted in PEOPLE — the NBA champion writes, “I have been obsessed with sex for as long as I can remember.”

“I am a sex addict,” writes Odom, who was married to Khloé Kardashian for four years before they split in 2013.

For more from Lamar Odom, pick up this week’s issue of PEOPLE, on newsstands Friday

The 39-year-old reveals that he has had sex with more than 2,000 women. “There were too many strippers to count,” he writes. “It wasn’t a big deal, but often I would pay them. I never thought less of them.”

Lamar Odom | Austin Hargrave

Odom also reveals that he cheated on Kardashian throughout their marriage; she eventually discovered the infidelities.

“I was shocked and embarrassed,” he tells PEOPLE in an exclusive interview. “I wanted to take it back, but you can’t. [I] wanted to hide it. But that sick sin was hard for me to hide … I had a problem.”

Kardashian’s rep did not respond to PEOPLE’s request for comment.

RELATED: Khloé Kardashian & Lamar Odom: A Timeline of Their Relationship

Khloé Kardashian and Lamar Odom | Kevin Mazur/Getty

Continues Odom: “[I] ran out of porn to watch! That’s how you know when you are going a little overboard.”

Odom’s addiction to sex was compounded by his addiction to drugs.

“Sex was a trigger for me to do drugs,” he tells PEOPLE. “Because you double up on [that] good feeling.”

Lamar Odom | Austin Hargrave

In 2015, Odom’s addictions led him to the Love Ranch brothel in Las Vegas, where he overdosed and nearly died.

“That was the wake-up call,” says Odom. “Like, this can’t happen again.”

RELATED: ‘I Was Doing Coke Every Day’: Lamar Odom Opens Up About Addiction After Overdose Almost Cost Him His Life

Darkness to Light

Now Odom is drug-free, but admits that he’s still working through his demons.

“I’m still an addict,” he writes in his book. “I still struggle … [But] I will not go into the darkness. Ever again.”

Darkness to Light is out May 28.