The couple will live in a large, comfortable but ordinary-looking house there.
A few loyalist onlookers called for Gyanendra to stay on as his car left but many in the crowd near the palace seemed happy to see him go, correspondents say.
"This marks the beginning of a new Nepal and the end of a dynasty that has done nothing but harm this country," Devendra Maharjan, a farmer who had come to Kathmandu to see the king leave the palace, told The Associated Press.
"If it had not been for the kings, Nepal would probably not have remained a poor nation."
Giving an unprecedented news conference at the palace earlier, the former monarch said he had given his priceless crown to the Nepalese government for its protection.
"I have no intention or thoughts to leave the country," Gyanendra said.
"I have assisted in and respected the verdict of the people."
He strongly rebuffed the suspicions of many Nepalis that he had engineered the palace massacre of 2001 which brought him to the throne.
He pointed out that his wife had had several bullets lodged in her body in the attack, in which Crown Prince Dipendra shot dead King Birendra and eight other members of the royal family before killing himself.
Gyanendra said he had taken over power in 2005 hoping it would bring harmony and peace, but he admitted things had not worked out as he had planned.
His stepmother and his grandfather's mistress will live on in their homes within the compound of the palace in central Kathmandu, in a fenced-off area.
The BBC's Charles Haviland in Kathmandu says that the former monarch's departure is a major symbolic moment in the fall of the Shah dynasty, which unified Nepal in the 1760s.
A supporter of the monarchy tried to stop Gyanendra's car leaving
The Maoists, who urged Gyanendra to bow out gracefully or be put on trial, welcomed the news that he was going quietly.
But the ending of the monarchy has generally been a bitter affair, our correspondent says.
It was engendered by the 2001 massacre and Gyanendra's attempts to be politically active in quelling the Maoist insurgency, he adds.
The deposed king is reported to be reluctant to allow a committee to audit his saleable assets.
He has made clear that he will leave behind most of the furniture in the palace, along with gifts he received in his capacity as the country's head of state.
Home Minister Krishna Prasad Sitaula said details of which possessions he keeps and which ones he leaves behind would be publicised after his departure from the palace.
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