It brings the controversial host's time on the show to an end after six years.
ITV announced the decision after Ofcom said it was investigating his comments after receiving 41,000 complaints.
On Monday's show, Morgan said he "didn't believe a word" the duchess had told Oprah Winfrey about her mental health in an interview.
An ITV spokesperson said: "Following discussions with ITV, Piers Morgan has decided now is the time to leave Good Morning Britain. ITV has accepted this decision and has nothing further to add."
The channel confirmed to the BBC that his departure from the breakfast news show will take effect immediately but declined to say who would be replacing him on Wednesday.
In a tweet on Wednesday morning Morgan said that he had reflected on his opinion on the Oprah interview and still did not believe Meghan, adding that "freedom of speech is a hill I'm happy to die on".
"Thanks for all the love, and hate. I'm off to spend more time with my opinions," he said.
Morgan's departure followed an on-air clash with weather presenter Alex Beresford, who criticised his colleague on Tuesday for "continuing to trash" the duchess, prompting Morgan to walk off set. He returned within 10 minutes.
Also on Tuesday, ITV chief executive Dame Carolyn McCall said she "completely believed what [the duchess] says", adding that ITV is "totally committed to" mental health.
Mental health charity Mind, which is a partner with ITV on its Britain Get Talking campaign, also criticised Morgan, saying it was "disappointed" by the presenter's comments.
On Monday's programme, Morgan picked up on the duchess's claim that her request to senior Buckingham Palace officials for help was rejected, after she told Oprah she had had suicidal thoughts.
"Who did you go to?" he said. "What did they say to you? I'm sorry, I don't believe a word she said, Meghan Markle. I wouldn't believe it if she read me a weather report.
"The fact that she's fired up this onslaught against our Royal Family I think is contemptible."
He also referred to the duchess as the "Pinocchio Princess" in a tweet later that morning.
Following an outcry, he said on Tuesday's episode that "I still have serious concerns about the veracity of a lot of what" Meghan said, but that it was "not for me to question if she felt suicidal".
He added: "My real concern was a disbelief frankly... that she went to a senior member of the Royal household and told them she was suicidal and was told she could not have any help because it would be a bad look for the family."
A total of 41,015 complaints were made to media watchdog Ofcom by 14:00 GMT on Tuesday.
That is the second highest number of complaints in Ofcom's 17-year history, behind the 44,500 submitted over several days about the racism row involving Jade Goody and Shilpa Shetty on Celebrity Big Brother in 2007.
"We have launched an investigation into Monday's episode of Good Morning Britain under our harm and offence rules," a spokesperson for the regulator said.
Meanwhile, on Monday evening Mind tweeted: "We were disappointed and concerned to see Piers Morgan's comments on not believing Meghan's experiences about suicidal thoughts today.
"It's vital that when people reach out for support or share their experiences of ill mental health that they are treated with dignity, respect and empathy. We are in conversations with ITV about this at the moment."
The baby Jesus was the last homeless person the Republicans liked.