Martinelli, who was accompanied by US officers, welcomed reporters gathered at the airport.
"I'm ready to watch the World Cup," Panama said.
Martinelli, 66, is accused of spying on contacts of more than 150 people, including journalists and politicians.
He faces an investigation in Panama in about 20 other corruption cases, but these cases were not mentioned in the extradition request.
Under an extradition treaty concluded in 1905, only the crimes contained in the extradition request can be tried in Panama.
His return to Panama comes at a time when the country is experiencing political unrest as it prepares for a general election in May.
The constitution prevents Martinelli from running for president by 2024. But he hopes to run for mayor or win a parliamentary seat, his spokesman Luis Eduardo Camacho said.
Martinelli was arrested in June 2017 and remained in Miami.
The former president insists he is a victim of "revenge" by President Juan Carlos Varela, his former deputy.