The Timesreport spurred Republican House Speaker Paul Ryan to call for an Ethics Committee investigation and Meehan's removal from the committee.
He is the fifth USA lawmaker to resign or say he will not run again amid a wave of sexual misconduct claims.
Meehan reportedly paid the settlement using his congressional office fund, which includes taxpayer money.
In the letter, Meehan also elaborated on his use of "soul mate", which drew widespread ridicule and anger - from political commentators to Stephen Colbert on The Late Show - after he and Daily News.
Meehan was booted from his post on the House Ethics Committee after the Timespublished a story on Saturday reached between Meehan and his former aide.
After an interview with The Inquirer where Meehan referred to the woman as his "soul mate" - all while saying that no romantic relationship had occurred - pressure ramped up on him to leave his seat. She says that he became hostile in the workplace when he discovered that she had entered a serious relationship with another man and did not reciprocate Meehan's feelings.
Meehan provided used public money to pay off a female staff member who filed the complaint.
Meehan, 62, is now subject to a review by the House Ethics Committee, which he sat on until the reports.
"I never in any way made any kind of pass towards her, I never discussed anything about wanting any kind of a further relationship, she's never alleged anything like that", Meehan said.
But he said in a letter sent to his campaign chairman on Thursday, he said that "recent events concerning my office and the settlement of certain harassment allegations have become a major distraction", according to Philadelphia Inquirer, which obtained a copy of the note.
Asked on CNN whether the party would continue to stand behind Meehan and put resources into his race, RNC chairwoman Ronna Romney McDaniel insisted "there's an investigation going on" and said she needed "to see more details".
Pennsylvania will now have at least four open seats in its Congressional delegation this November: Meehan in the 7th, Rep. Bill Shuster in the 9th, Rep. Lou Barletta in the 11th, and Rep. Charlie Dent in the 15th. Now with Meehan not seeking re-election, the field could grow even bigger.
Gale previously chaired and managed his brother's county commissioner campaign and orchestrated Republican Stan Casacio's unsuccessful 2016 primary election challenge for the 7th District seat, according to the release.
Andy Murray looks to sport management role for future talent
He says that he still wishes to compete in professional tennis but he also wants to expand his prospects and share his knowledge. At the moment he is juggling many balls and he wants to remain focused on what he knows, but over time his company will develop.