Two United States police officers took charge of the 57-year-old accountant and escorted him onto a flight bound for New York.
Takkas, born in Cyprus and holding Greek and British nationalities, was one of six FIFA officials arrested in May 2015 at the request of American authorities. Swiss officials then rubber stamped his extradition in October.
After three appeals failed, the final one on March 3rd, Takkas decided against a final appeal.
Of those arrested only former Nicaraguan federation president Julio Rocha remains detained in Switzerland but he has just 10 days remaining to appeal and stave off his own extradition.
The six are part of a group of 39 officials and marketing executives accused by US prosecutors of soliciting and receiving tens of millions of dollars in bribes and kickbacks in a case that has sparked an unprecedented crisis at FIFA.