The lawyers told AFP the US State Department had signed off on the extradition after rejecting Martinelli's argument that he faced a risk of being tortured if returned to Panama.
Martinelli's spokesman Luis Eduardo Camacho told AFP that he believed the extradition would be carried out "pretty quickly" over the coming days, without offering a precise date.
Martinelli, who served as president from 2009 to 2014, was accused of spying on the telephone calls of more than 150 people, including journalists and politicians.
He is under investigation in Panama in about 20 other cases of corruption, but those are not referred to in the extradition request.
Under a 1905 extradition treaty, he can only be tried in Panama for the crimes alleged in the request.
In Panama, President Juan Carlos Varela confirmed his government had been notified of the State Department action and pledged "everything will be managed on the basis of the proceedings, laws and constitution of the country."
Martinelli, 66, was detained in June last year and has been incarcerated in Miami since then.
Having exhausted his appeals, his fate was left in the hands of the US government.
On May 15, his lawyers submitted a 430-page document to the State Department in which they asked Secretary of State Mike Pompeo to exercise his discretion and deny Panama's "politically motivated" extradition request.
Martinelli argued he was the victim of a "vendetta" by Varela, his former vice president.
In an open letter that his lawyers made public last month, Martinelli cited occasions when he had done favors for the United States.
"When the CIA requested that I stop a North Korean ship leaving Cuba that was crossing the Panama Canal, I did not blink an eye," he wrote.
That was a reference to the North Korean cargo ship, Chong Chon Gang, seized in 2013 with undeclared missile system components aboard, in an apparent breach of UN sanctions.
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