The US state department said Saleh's request for a visa "has been approved".
"As we have indicated, 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," it said in a statement on Sunday.
A Sanaa airport official said Saleh's plane took off in the evening.
The Yemeni news website Mareb Press quoted an unidentified source at the airport as saying Saleh left on a private Saudi plane a few hours after his family's departure.
"God willing, I will leave for treatment in the United States and I will return to Sanaa as head of the General People's Congress party," Saleh was quoted by the state news agency, SABA, as telling a meeting with party officials on Sunday.
"I ask for forgiveness from all my people, men and women, for any shortcomings during my 33-year-long rule," he said.
While an aide to Saleh said he would stay there in Oman for several days before heading to the US, an Omani official told the Reuters news agency that he would be in transit for only a few hours.
Diplomats in Sanaa said that Saleh's eldest son Ahmed - who commands the Republican Guard - was "already in Oman" to prepare for his father's arrival.
Sultan al-Barakani, a senior official of the GPC party, said last week that the 69-year-old president would visit Oman and then Ethiopia before travelling to New York for treatment for wounds he sustained in a bombing at the presidential palace last June.