Everson, the former commissioner of the U.S. Internal Revenue Service, took the Red Cross job last May as the charity sought to restructure itself after sharp criticism of its response to Hurricane Katrina.
In a statement, the Red Cross said its board of governors asked for and received Everson's resignation, effective immediately, after learning within the past two weeks of the relationship with a woman on the Red Cross staff. The woman was not identified.
"The board acted quickly after learning that Mr. Everson engaged in a personal relationship with a subordinate employee," the statement said. "It concluded that the situation reflected poor judgment on Mr. Everson's part and diminished his ability to lead the organization in the future."
The Red Cross also released a statement from Everson, who is married and has two children.
"I am resigning for personal and family reasons, and deeply regret it is impossible for me to continue a job so recently undertaken," he said. "I leave with extraordinary admiration for the American Red Cross."
The charity's board appointed Mary S. Elcano, its general counsel for the past five years, as interim president and CEO. Elcano's past experience includes a stint as executive vice president of human resources with the U.S. Postal Service.
"Although this is difficult and disappointing news for the Red Cross community, the organization remains strong and the lifesaving mission and work of the American Red Cross will go forward," said the board's chair, Bonnie McElveen-Hunter.
She said a search committee has been formed to seek a new leader.
The development was a blow to the Red Cross as it was making progress in overcoming image problems arising from its response to Katrina and the Sept. 11, 2001, terror attacks. Addressing complaints that it was at times too bureaucratic and unaccountable, the charity overhauled its disaster-response system and the way it governs itself, and it was praised for its role during the recent Southern California wildfires.
"This does not reflect on the organization," Red Cross spokeswoman Suzy DeFrancis said of Everson's ouster. "People felt we were moving forward."
Everson's departure continues a trend of rapid turnover atop the Red Cross. The two women who preceded him as president both resigned amid friction with the board of governors Bernadette Healy after the Sept. 11 attacks and Marsha Evans in 2005, after Katrina. An interim president, Jack McGuire, served between Evan's departure and Everson's appointment.
When he took the Red Cross job, Everson embraced it after four years running the Internal Revenue Service.
"My 18-year-old daughter said, 'People will like you now,"' Everson remarked during an interview in July with The Associated Press.