The change of leadership was announced by publisher of the paper and chairman of The New York Times Company Arthur Sulzberger, who told a "stunned newsroom"that he had made the decision because of "an issue with management in the newsroom."
Abramson, 60, was named executive editor had been only in September 2011.
A report in the NYT said according to people briefed on the situation, there was serious tension in Abramson's relationship with Sulzberger,who had concerns about complaints from employees that she was polarising and mercurial.
In recent weeks, Baquet had also become angered over a decision by Abramson to offer a job to a senior editor from The Guardian, Janine Gibson, as co-managingeditor without consulting him.
The decision to dismiss Abramson was made by Sulzberger earlier this month and he informed Baquet of his promotion last week, according to the people briefed onthe situation.
The editorial upheaval comes in a crucial year for The Times, which had to shed assets like The Boston Globe and About.com.
In accepting the job, Baquet, 57, said, "I will listen hard, I will be hands on, I will be engaged. Ill walk the room," he said. "That's the only way I know how to edit."
Baquet had first joined The Times in April 1990 as a metropolitan reporter.
He previously worked for The Times-Picayune in New Orleans for nearly seven years and for The Chicago Tribune, where he won a Pulitzer Prize for investigative reporting in 1988.
He had served as managing editor and editor of The Los Angeles Times before rejoining the Times in 2007, where he served as an assistant managing editorand Washington bureau chief.
In a prepared statement, Abramson said "I've loved my run at The Times. I got to work with the best journalists in the world doing so much stand-up journalism."
Abramson had called being appointed as the paper's top editor as "the honor of my life" and had even got a tattoo of the newspapers gothic "T" on her back.
The Times won eight Pulitzer Prizes under Abramson, who had previously served as the head of NYT's Washington bureau and as an investigative reporter at The Wall Street Journal.