US President George W Bush cut short a Texas vacation and flew back to Washington to sign the bill as soon as it has passed both houses of Congress.
“This is about defending life,” White House spokesman Scott McClellan said.
“The president intends to sign legislation as quickly as possible once it is passed,” he said.
The House of Representatives is expected to pass the bill on Monday.
Terri Schiavo, 41, is severely brain damaged and has been in a vegetative state since her heart stopped in 1990.
Her husband Michael Schiavo, who says his wife would want to die, has been fighting a bitter legal battle in the Florida courts with Ms Schiavo’s parents and siblings, who want to keep her alive.
On Friday a Florida court ordered Ms Schiavo’s feeding tubes be removed, at the request of her husband and guardian.
Experts say that without food and liquid, she will die in about two weeks.
But in an unprecedented move, the case was taken up by Republican law-makers in Washington.
Congress – where Republicans hold the majority — scheduled a rare emergency session on Sunday to pass legislation.
Congressional leaders delayed Sunday’s debate after objections from Democrats.
The case has ignited a fierce debate over euthanasia in the United States, with right-to-life campaigners pitted against the pro-euthanasia lobby.
Mr Bush’s brother, Florida Governor Jeb Bush, has intervened to stop Ms Schiavo’s euthanasia in the past, and her feeding tube have been removed and reattached on previous occasions.
Critics say Congress is setting a dangerous precedent for the federal government to intervene in court decisions and private family matters.
“For Congress to come in and interfere in a personal family matter is outrageous. They can do it to me, they’ll do it to every person in this country,” Michael Schiavo said on US television.