The Amazon.com chief, who purchased the newspaper for $250 million last summer, informed the 48-year-old Weymouth he had selected a new publisher on Aug. 18, the newspaper said.
Read MoreAmazon CEO Jeff Bezos buying The Washington Post
Weymouth's great-grandfather bought the paper in 1933 at a bankruptcy auction.
Ryan became a top aide to Reagan and was instrumental in building the Reagan Presidential Library.
"You don't shrink your way to success," Ryan said. "The Post is on the move. There's no question about that."
Read MoreThe Washington Post and Jeff Bezos' 'to do' list
Ryan said he plans to keep Martin Baron as executive editor and Fred Hiatt as editorial page editor. He also said he did not anticipate changes in editorial policies and would protect the independence of the newsroom.
To read the Post's full story, click here.
—By CNBC.com staff