Mr Yarrington, who served as governor from 1999 to 2005, had been on the run for almost five years.
Officials did not reveal how they located Mr Yarrington.
The attorney-general’s office in Mexico said Mr Yarrington would be extradited to his homeland within days.
‘Cocaine for access’
In return, Mr Yarrington allegedly allowed the cartels “to operate their large-scale, multi-tonne enterprises freely, which included the smuggling of large quantities of drugs to the US for distribution”.
Prosecutors say the bribes started when Mr Yarrington was running for governor and continued during his time in office, when he allegedly started investing the money in properties across the US border in Texas.
The indictment also accuses him of accepting cocaine in exchange for facilitating access to Mexican ports.
Before he went on the run, Mr Yarrington, who was a member of the governing PRI party before being expelled, said the charges against him were politically motivated.
He was not the only Mexican governor on the run.
And in March, the ex-governor of Chihuahua, César Duarte, was declared a fugitive after he disappeared following allegations of corruption.
Both were expelled from the PRI party when the charges against them became known.