Sources familiar with the probe had previously told ABC News that Laurean boarded a bus in Raleigh-Durham, N.C., and then rode to Houston. In Houston, he allegedly boarded another bus and then traveled to San Luis Potosi, a state in central Mexico.
Sources say U.S. authorities tracked his general location by triangulating cell phone and other electronic communications.
Laurean was born in Mexico, but became a naturalized U.S. citizen in 2003. It's not known whether he retained his Mexican citizenship, although investigators have said that he has family in Mexico.
As of Friday, authorities are holding Laurean in Mexico City. "Extradition proceedings will follow their normal course," Mexican Ambassador to the United States Arturo Sarukhan said in a statement to ABC News, "but the arrest underscores Mexico's commitment with the rule of law and to fully cooperate with the United States on all law enforcement issues."
"It highlights our strong determination to make Mexican territory an ill-fitted choice for any fugitive seeking a safe haven from justice," the statement continued.
Local, state, federal and military investigators worked with Interpol and the Mexican government coordinated the manhunt.
"The FBI and its law enforcement partners brought to bear all of our domestic and international resources to find a man wanted for murder. Laurean's swift arrest in Mexico was due to the diligence and dedication of the Mexican government and our law enforcement partners," Nathan Gray, the FBI special agent in charge, said in a statement released Thursday.
An attorney for Lauterbach's family said the victim's mother received a call from the FBI confirming the capture around 9 p.m. Thursday.
''She's been living with Cpl. Laurean being on the run … and living without an expectation that he was going to be captured any time soon, so when the word came it really caught her by surprise, and she's still trying to let it all sink in,'' family lawyer Merle Wilberding told WDTN-TV in Dayton, Ohio.