The 53-year-old called his behaviour at the Academy Awards “unacceptable and inexcusable” and said he was embarrassed by his actions.
Smith added that the joke about his wife’s medical condition had caused him to react “emotionally” but “violence in all its forms is poisonous and destructive”.
In a statement posted to Instagram the actor said: “I would like to publicly apologise to you, Chris. I was out of line and I was wrong.
“I am embarrassed and my actions were not indicative of the man I want to be. There is no place for violence in a world of love and kindness.
“I would also like to apologise to the Academy, the producers of the show, all the attendees and everyone watching around the world. I would like to apologise to the Williams Family and my King Richard Family.
“I deeply regret that my behaviour has stained what has been an otherwise gorgeous journey for all of us.”
Smith concluded his apology by saying: “I am a work in progress.”
Smith has been condemned by the Academy as it launched a formal review into his altercation with Rock during the Oscars ceremony.
The 94th annual awards show was thrown into chaos when Smith went onstage and hit the comedian in front of a star-studded audience, after Rock made a joke about his wife Jada Pinkett Smith and her hair loss.
Rock had compared Smith’s wife – who suffers from the medical condition alopecia – to “GI Jane”.
Smith, who won his first Academy Award for King Richard, appeared to take offence to a gag Rock made about Pinkett Smith’s short haircut.
The Magic Mike XXL star and Red Table Talk host has previously spoken about her struggles with alopecia and said it is what prompted her to shave her head.
Referring to Pinkett Smith’s buzzcut, Rock said: “Jada, can’t wait for GI Jane 2,” prompting the actress to roll her eyes.
However, Smith walked up on stage and hit Rock before returning to his seat and shouting twice: “Keep my wife’s name out of your f****** mouth.”
The altercation left Rock shocked and flustered as he tried to resume presenting the best documentary feature category.
In a statement on Monday, the film academy said: “The Academy condemns the actions of Mr Smith at last night’s show.
“We have officially started a formal review around the incident and will explore further action and consequences in accordance with our bylaws, standards of conduct and California law.”
As he collected his gong, Smith apologised to the Academy and his fellow nominees, but not to Rock, joking that he “looks like the crazy father”.
Breaking down in tears, he said: “Richard Williams was a fierce defender of his family.
“I’m being called on in my life to love people and to protect people and to be a river to my people.
“I know to do what we do you’ve got to be able to take abuse, you’ve got to be able to have people talk crazy about you in this business.
“You’ve got to be able have people disrespecting you and you’ve got to smile and pretend like that’s OK.
“I want to apologise to the Academy, I want to apologise to all my fellow nominees.
“Art imitates life, I look like the crazy father, just like they said about Richard Williams, but love will make you do crazy things.”
He concluded by saying he hoped the Academy invited him back in future.
The Academy later said it did not “condone violence of any form” in a tweet posted from its official account.
The Los Angeles Police Department (LAPD) said no report had been filed after the incident.
“LAPD investigative entities are aware of an incident between two individuals during the Academy Awards programme,” a spokesperson for the force told the PA news agency.
“The incident involved one individual slapping another. The individual involved has declined to file a police report.
“If the involved party desires a police report at a later date, LAPD will be available to complete an investigative report.”
Oscars showrunner Will Packer later described the altercation as “a very painful moment for me”.
He initially responded to the incident by saying: “Welp… I said it wouldn’t be boring #Oscars,” a comment that drew some criticism.
He later tweeted: “Black people have a defiant spirit of laughter when it comes to dealing with pain because there has been so much of it. I don’t feel the need to elucidate that for you.
“But I also don’t mind being transparent and say that this was a very painful moment for me. On many levels.”