Mr Harman made his money originally by selling stereo equipment. He is married to longstanding Californian Congresswoman Jane Harman, known for her strong support of Israel.
Donald E Graham, chairman of the Washington Post Company, said: “In seeking a buyer we wanted someone who feels as strongly as we do about the importance of quality journalism.
“We found that person in Sidney Harman.
“He is a quality man, a man who cares, and a man who will be trying with all his power to shape a successful future for Newsweek."
Mr Harman said: "I would be delighted over a period of a few years to see Newsweek get by on its own fuel.”
But he added: “I’m not here to make money. I’m here to make joy.”