The company didn't give a reason for the change. Abramson and Baquet had both been in their current positions since September 2011.
Baquet, 57, who would be the first African-American to hold the newspaper's highest editorial position, received a Pulitzer Prize for investigative reporting in 1988.
"It is an honor to be asked to lead the only newsroom in the country that is actually better than it was a generation ago, one that approaches the world with wonder and ambition every day," Baquet said in a statement released by the newspaper.
The move comes amid a continued shift in the Times' focus, and that of the newspaper industry overall, toward digital products and away from traditional print papers as print circulation and advertising revenue declines.
Arthur Sulzberger Jr., the newspaper's publisher and chairman of its parent company, called Baquet the best qualified journalist to take on the job in the Times' newsroom.
"He is an exceptional reporter and editor with impeccable news judgment who enjoys the confidence and support of his colleagues around the world and across the organization," Sulzberger said in a statement.
Baquet originally joined the Times in 1990 as a reporter and held positions including deputy metropolitan editor and national editor. He left the paper for the Los Angeles Times in 2000, where he served as managing editor and then editor. Baquet rejoined the Times in 2007 and was Washington bureau chief before becoming the managing editor for news in September 2011.
Prior to his first stint at the Times, Baquet worked at The Chicago Tribune and The Times Picayune in New Orleans. While at the Tribune in 1988, he and two other journalists won the Pulitzer Prize for investigative reporting, for looking into corruption in the Chicago City Council. He was a finalist in the same category in 1994.
Abramson, 60, was the paper's first female executive editor. She joined the newspaper in 1997 after working for nearly a decade at The Wall Street Journal. She was the Times' Washington editor and bureau chief before being named managing editor in 2003.
Baquet succeeded her as managing editor after she was named to the top editing spot.
New York Times Co. shares fell 66 cents, or 4.2 percent, to $15.11 in afternoon trading.
Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.