In addition, AMI has the right to publish five health and fitness columns under McDougal's byline and to feature her on the cover of Men's Journal.
Cameron Stracher, general counsel for AMI, said the company intends for McDougal to appear on the September 2018 issue of the magazine.
Under the terms of the deal, McDougal and AMI must each pay their own lawyers' fees.
Both sides called the deal a victory.
"From our perspective, it's a complete win," Stracher said. "We got out of a lawsuit without paying a dime, she got out of a lawsuit without paying a dime, and everyone's happy and gets to go on their way."
In a statement, McDougal said she was "relieved to be able to tell the truth about my story when asked."
"My goal from the beginning was to restore my rights and not to achieve any financial gain, and this settlement does exactly that," she said.
In an extended interview with CNN last month, McDougal said that she and Trump had a 10-month relationship in 2006 and 2007, during which they met dozens of times at multiple Trump properties - including the apartment he shared with his wife, Melania. Their son was an infant at the time.
McDougal alleged in her lawsuit that AMI bought her story in August 2016 not to publish it but to bury it - an outcome she said she welcomed at the time because she did not want her story made public.
But she said her perspective changed after new details emerged about the deal in the news media, particularly communication between the lawyer who negotiated the contract on her behalf, Keith Davidson, and Cohen, who had no formal role in the deal, as well as between AMI - which is led by David Pecker, a friend of Trump's - and Cohen.
Her lawsuit named neither Davidson and Cohen as defendants but alleged they colluded to reach a deal that would bury McDougal's allegations.
AMI had asked the court to dismiss McDougal's complaint, arguing that the deal was protected under the First Amendment.
McDougal's settlement with AMI says that while she releases all claims against the tabloid company, she does not release any claims that she "has or may have" against Cohen and Davidson.
Davidson has said he fulfilled his obligations as a lawyer and "zealously advocated" to accomplish McDougal's goals at the time. Cohen's lawyer, Brent Blakely, did not immediately return a call seeking comment Wednesday.
AMI and Trump still face complaints the government watchdog group Common Cause filed with the Federal Election Commission and the Justice Department, alleging that the agreement with McDougal amounted to an illegal in-kind campaign contribution to Trump.
