A Yemeni government spokesman, Mohammed Albasha, confirmed that Mr. Saleh had left the country but provided no further details. 
A high-ranking official said that Mr. Saleh was to stop first in the neighboring country of Oman, and then continue to the United States, where he is expected to arrive by Wednesday.
The Dubai-based television network al Arabiya reported Sunday evening that Mr. Saleh had landed in Oman.
The Yemeni official, who spoke on the condition of anonymity because he was not authorized to speak to the news media, said that Mr. Saleh was reluctant to travel, but required treatment outside the country for injuries, including extensive burns, he sustained in a bomb attack on the presidential palace in June.
The State Department said the Obama administration had approved his visit. The department said in a statement that “the sole purpose of this travel is for medical treatment and we expect that he will stay for a limited time that corresponds to the duration of this treatment.”
The statement’s careful wording reflected the vigorous debate within the administration over whether to admit Mr. Saleh, a longtime American ally, and risk appearing to harbor an authoritarian leader accused of responsibility for the deaths of hundreds of antigovernment protesters.
In making their decision, administration officials cited the advantages of having Mr. Saleh leave the country before the presidential election scheduled for Feb. 21.
Mr. Saleh, who has faced a year of protests and international pressure calling for the end of his 33-year rule, had previously made contradictory statements about whether he would leave the county and when he would leave office. In December, he said he was leaving Yemen for treatment in the United States, and then reversed himself two weeks later.
In a televised speech on Sunday, described as a farewell address, he said he would return to Yemen when his treatment was finished.
Although he has agreed to leave office, he said in the speech that he was handing power to his vice president, Abdel Rabbo Mansour Hadi, temporarily.
“I entrusted all my powers to the vice president,” Mr. Saleh said. “He bears responsibility until elections on 21 February.”
Mr. Saleh also asked the nation’s “pardon for any failure that occurred during my tenure.” 
He agreed to step down in November in exchange for immunity from prosecution, in a deal brokered by Gulf countries. Protesters and human rights groups have demanded that he be tried for the deaths of protesters killed by his security forces and pro-government militias.
On Saturday, Parliament passed a law granting him immunity, and extending the immunity to subordinates who committed politically motivated crimes. Parliament also approved Vice President Hadi as the consensus candidate, agreed on by Mr. Saleh’s party and the opposition, for the presidential election.
Mr. Saleh handed over some of his duties to Mr. Hadi after he signed the agreement in November, but has continued to wield power. He is supposed to officially step down from office after the election of a new president.
When the Obama administration decided to admit Mr. Saleh last month, an official said that he would be treated at NewYork-Presbyterian Hospital.
However, a spokeswoman for the hospital, Myrna Manners, said Sunday that there were “no current plans” for him to be admitted there.
The hospital is renowned for its burn center, one of the busiest in the country, which conducts research on advanced treatment of burns.
In his speech on Sunday, Mr. Saleh called for reconciliation and urged Yemenis to work together to reconstruct their country. Speaking directly to the protesters who have been camped out in sit-ins across the country for nearly a year, he said, “Go back to your homes, go back to your families.”
“I feel sorry for you and invite you to return to your house and start with a new page with the new leadership,” he said.
The protesters, however, saw Mr. Saleh’s departure as only one step toward dismantling the regime he built and which his family and loyalists still control.
“It is a positive thing and pushes forward our revolution’s goals,” said Salah al-Nagb, a youth activist at a sit-in in Sana. “We will continue the work of our revolution at the same pace in order to overthrow this corrupt regime, not just one individual, but the whole regime.” 
Anemona Hartocollis and Yasser Alarami contributed reporting.
This article has been revised to reflect the following correction:
Correction: January 23, 2012
A previous version of this article misspelled the first name of a Yemeni government spokesman. It is Mohammed Albasha, not Muhammad Albasha.