Laurean was found in Tacambaro, Mexico at about 7pm Thursday night.
FBI agents and Mexican authorities made the arrest, after a 3 month-long international man-hunt.
Lauterbach accused him of rape last year, but it's unclear if her unborn baby was his.
Investigators found her charred remains in Laurean's back yard in Onslow County in January. By that time, Laurean had already disappeared.
21-year-old Laurean now awaits extradition back to Onslow County.
Although Laurean has been captured local prosecutors say the process could take a year or more.
A news conference on his capture is scheduled for Friday, April 11th.
PRESS REALEASE FROM THURSDAY'S FBI CAPTURE FOLLOWS
The Marine corporal is a suspect in the death of Maria Lauterbauch. Her body and a fetus was found charred and buried in a pit behind the Corporal's Onslow County home Saturday.
The search for Marine Cpl. Cesar Armando Laurean entered its fourth day Tuesday with a $25,000 reward and a plan to post billboards of his picture nationwide.
"The search for Laurean is Earthwide," Onslow County Sheriff Ed Brown said Monday. "It may be two days or two weeks, 10 days or 10 years, but you're never gone for good."
Lauterbach disappeared sometime after Dec. 14. The 20-year-old Dayton native had recently met with military prosecutors to talk about her April allegation that Laurean raped her.
Over the weekend, authorities recovered what they believe to be the burned remains of Lauterbach and her unborn child from a fire pit in Laurean's backyard in Jacksonville, N.C.
On Saturday, authorities issued an arrest warrant on murder charges for Laurean, 21, of the Las Vegas area. They believe he fled Jacksonville before dawn on Friday, leaving behind a note in which he admitted to burying her body but said Lauterbach cut her own throat in a suicide.
Brown, who has rejected the idea that Lauterbach committed suicide, said late Monday that authorities had received a preliminary autopsy report on the remains. He declined to discuss details, other than to say a gun was not used.
Lauterbach's military ID card was found at a bus station in Durham, about 150 miles northwest of Jacksonville. Witnesses reported seeing his black four-door pickup truck in the Raleigh and Durham area, Brown said.
Other witnesses said they thought they saw him Saturday night at a bus station in Shreveport, La.
Police found Laurean's truck outside a Morrisville hotel on Airport Blvd. late Tuesday afternoon. Laurean remains missing. Onslow County investigators are on their way to Morrisville to conduct test on the vehicle.
The FBI and United States Marshals are involved in the search for Laurean, who is expected to be charged with murder when he is arrested. The first billboards with Laurean's photo went up in Columbus, Ohio, and others are expected in Tampa, Fla., and Las Vegas.
The military could seek charges at the same time as civilian authorities, said Scott Silliman, a former military lawyer who is now director of the Center on Law, Ethics and National Security at Duke University. But a joint prosecution is not recommended by the military's manual for courts-martial, Silliman said.
North Carolina is one of 15 states without a fetal homicide law, but Onslow County District Attorney Dewey Hudson said he has no plans to step aside in favor of a military prosecution.
Anyone with information about the whereabouts of Laurean, call 1-800-callfbi.
