WASHINGTON — Janet L. Yellen, chairwoman of the Federal Reserve, said on Monday that she would step down from the Fed’s board at the same time that she ends her term as chairwoman.

President Trump decided earlier this month to nominate Jerome H. Powell, a Republican who sits on the Fed’s board, as the next chairman, deciding against offering Ms. Yellen a second term. Ms. Yellen, whose term as chairwoman ends in February, could have remained on the Fed board until her term as governor expires in 2024.

Her decision to step down instead had been widely expected, though some Democrats had argued publicly and privately that she could best defend her legacy from the inside.

“I am gratified that the financial system is much stronger than a decade ago, better able to withstand future bouts of instability and continue supporting the economic aspirations of American families and businesses,” Ms. Yellen wrote Monday in a letter to President Trump announcing her decision. “I am also gratified by the substantial improvement in the economy since the crisis.”