Weymouth is the granddaughter of the late Katharine Graham, the former chairwoman of The Washington Post Co. who held that position from 1973 until 1991. She is also the fifth member of the Graham family to head the business.
Weymouth, 41, succeeds Boisfeuillet Jones, Jr., 61, who has been publisher of the Post since 2000.
She has worked at the newspaper since 1996 and served as vice president of advertising since 2005, The Washington Post reported.
She comes on board at a time of declining newspaper sales. Circulation at the Post has declined from a peak of 832,232 in 1993 to 638,000.
"Katharine is ready for this," said her uncle, Donald Graham, chairman of The Washington Post Co. "She's Kay Graham's granddaughter, but that's not why she's getting this job."
"While it's humbling to follow in the footsteps of my ancestors, it is also very exciting. I will do my best to honor their legacy,'' said Weymouth.
That legacy began with her great-grandfather Eugene Meyer, who purchased the newspaper in 1933, the Post said.