Tristan Thompson has apologised to Khloe Kardashian for causing her "heartache and humiliation" after a paternity test revealed he has fathered a child with another woman.

The basketball star said he was "so incredibly sorry" for his actions in a social media post that addressed the reality star directly.

Their relationship has been on-off and a cheating scandal involving Thompson featured in later seasons of the long-running reality show Keeping Up With The Kardashians.

"Today, paternity test results revealed that I fathered a child with Maralee Nichols," he said in an Instagram story. I take full responsibility for my actions.

"Now that paternity has been established I look forward to amicably raising our son.

Tristan Thompson and Khloe Kardashian

"I sincerely apologise to everyone I've hurt or disappointed throughout this ordeal both publicly and privately."

He continued: "Khloe, you don’t deserve the heartache and humiliation my actions have caused you. You don’t deserve the way I have treated you over the years. My actions certainly have not lined up with the way I view you.

"I have the utmost respect and love for you. Regardless of what you may think.

"Again, I am so incredibly sorry."

Kardashian shares a three-year-old daughter True with basketball star Thompson.