Mr Trump, whose campaign has been complicated by dozens of charges, for months said he did not need to attend the event.
“The public knows who I am and what a successful presidency I had, with energy independence, strong borders and military, biggest ever tax and regulation cuts, no inflation, strongest economy in history and much more,” Mr Trump wrote on his social media site, Truth Social.
“I will therefore not be doing the debates.”
The first Republican debate for the 2024 presidential race will take place on Wednesday, in Milwaukee, Wisconsin.
Mr Trump referred to a CBS poll released on Sunday that showed him leading among Republican candidates by 62 per cent.
His closest competitor, Florida Governor Ron DeSantis, has 16 per cent support, the poll showed. The remaining contenders were in the single digits.
On Friday, The New York Times reported that Mr Trump was instead planning to appear for an interview with Tucker Carlson, the former Fox News host, who now has a show on X, formerly known as Twitter.
Chris Christie, a Republican hopeful who has sharply criticised Mr Trump in the past, lambasted the former president.
"Surprise, surprise … the guy who is out on bail from four jurisdictions and can’t defend his reprehensible conduct, is running scared and hiding from the debate stage," Mr Christie wrote on X.
"Trump – certified loser, verified coward."
Mr Trump has until Friday to turn himself in to authorities and face accusations that he and 18 allies conspired to overturn the results of the 2020 elections in Georgia, a state he narrowly lost to Joe Biden.
Court filings on Monday revealed that Mr Trump's bail is set at $200,000 and bars him from intimidating co-defendants, witnesses or victims in the case, including on social media.
The indictment in Georgia is his fourth this year, and adds to his increasingly complicated legal troubles in the lead-up to the 2024 presidential campaign.
Mr Trump faces dozens of charges involving allegations that he tried to overturn the results of the 2020 presidential election, mishandled classified documents and was involved in hush-money payments to an adult film actress.
He has also been charged in federal court in a plot to undermine democracy for his actions before the January 6 riot at the Capitol in 2021.
The US Justice Department's special counsel has proposed January 2 next year as a trial date to face those charges, his most serious, but Mr Trump's lawyers last week asked for it to be pushed back to April 2026.
He has called the cases against him "witch hunts" and politically motivated to undermine him.