Martinelli, 66, was Panama's president from 2009 to 2014.
Martinelli was imprisoned in the United States past year after Panama requested the extradition on charges that he used public money to spy on more than 150 political opponents in the period of 2009-2014.
On Monday a handcuffed Martinelli, escorted by US Marshals, greeted reporters gathered to see him off at the Miami-area airport. Panama qualified for the tournament, which begins on Thursday.
Trump says North Korea no longer a nuclear threat
The US President also said that sanctions will remain in place until Pyangyong halts and dismantles its nuclear programme. Trump phoned South Korean President Moon Jae-in after leaving Singapore to brief him on the discussions.
According to a statement by the Justice Department, Martinelli was indicted in Panama for illicitly monitoring the private communications of more than 150 people he identified as "targets" through the use of two multi-million dollar surveillance systems.
Under a 1905 extradition treaty, he can only be tried in Panama for the crimes alleged in the request.
The former President was arrested in June of 2017, not far from Miami, where he lived after leaving Panama in 2015. They did not give details of his arrival, but dozens of Martinelli's supporters gathered at the Tocumen global airport, waving flags of the political party the former president founded, local television footage showed.
Mr Martinelli is being sent to the same prison where Panama's former military leader, General Manuel Noriega, spent the last years of his life.
Martinelli is barred by term limits from running for president before 2024, but he hopes to run for a mayorship or a congressional seat, his spokesman Luis Eduardo Camacho has said.