Mr Yarrington, who served as governor from 1999 to 2005, had been on the run for almost five years.
The ex-governor is accused of taking millions of dollars in bribes from drug cartels in return for turning a blind eye to their smuggling activities.
A reward of 15m Mexican pesos ($800,000; £650,000) had been offered for information leading to his arrest.
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.
He is also wanted by the United States on charges of money laundering.
According to the US indictment, Mr Yarrington allegedly received large bribes from major drug traffickers operating in Tamaulipas, including the Gulf and the Zetas cartels.
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.
Former Veracruz governor Javier Duarte, who is wanted on corruption charges, has been missing since October.
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.

About 1,000 people gathered to observe a minute of silence and light candles in front of the Senedd.
There are over 2,000 French people living in south Wales registered with the French consulate in London.
Marie Brousseau-Navarro, the Honorary Consul of France in Cardiff, said messages of support had been touching.
She said: "We are united in shock and united in sorrow... And united with all the people who have marched across the world."
Saleem Kidwai, chairman of the Muslim Council of Wales was applauded by the crowd as he told them to "stand together shoulder to shoulder".
"My condemnation is absolute," he said.
"We will eventually win and truth wins over falsehood and light over darkness."
First Minister Carwyn Jones was among the many to hold up a candle for the silence, while others held up pencils. The silence was marked at the end by an applause.
Earlier, he said: "The vigil in Cardiff Bay tonight is an opportunity for the people of Wales to pay their respects to those who lost their lives in the truly abhorrent attack in Paris.
"It is also a chance to show solidarity with the people of France and all those who believe in upholding our democratic values and freedoms that are threatened by such senseless acts of terror."
Welsh Secretary Stephen Crabb tweeted earlier: "Standing with the French community in Wales and in support of freedom of speech everywhere. 6pm this eve. Senedd, Cardiff. #CharlieHebdo"
In a show of unity, London landmarks have been lit in the colours of the French national flag.
And world leaders have gathered in Paris for a huge unity march involving over one million people, dwarfing Saturday's marches that saw 700,000 take to the streets.
On Saturday, Swansea City striker Bafetimbi Gomis dedicated his side's goal in the 1-1 draw with West Ham to the victims of the Paris terror attacks.
Wales' police forces and media organisations held a minute's silence to support those attacked in the Charlie Hebdo massacre in Paris on Wednesday.
A police officer was killed on Thursday and French forces stormed two separate hostage sites in and around Paris, killing three hostage takers, on Friday.
"We have been really moved by the hundreds of messages of support and condolences," said Ms Brousseau-Navarro.
"Most of all we appreciate the support and solidarity."
Police in Italy have arrested the former governor of the Mexican state of Tamaulipas, Tomás Yarrington, 59.
[NEXT_CONCEPT]
A vigil has taken place in Cardiff Bay for French citizens and others following terror acts in Paris which left 17 people dead in three days.