Armstrong is expected to see a judge in Houston before being transferred to Austin.
The 34-year-old Armstrong is accused of fatally shooting 25-year-old Anna Moriah Wilson at a home in Austin in May.
According to court documents, airline records show Armstrong flew from Austin to Houston on a Southwest Airlines flight on May 14. In Houston, she then connected to a flight at La Guardia in New York City.
Investigators believe she then flew to Costa Rica.
Agents say they were able to track Armstrong down and capture her at a hostel on Santa Teresa Beach on June 29.
"We know that she registered at specific yoga studios based on communication that was brought back to us here in the United States. So we knew she had a pattern of life, she was trying to extend that career possibly to be a yoga instructor, to get the knowledge of it," said Deputy Brandon Filla with the U.S. Marshal Service.
"The Marshals Service elevated the Kaitlin Armstrong investigation to major case status early in this investigation, which likely played a key role in her capture after a 43-day run,” said Susan Pamerleau, U.S. Marshal for the Western District of Texas. “This is an example of combining the resources of local, state, federal and international authorities to apprehend a violent fugitive, bring an end to that run and hopefully a sense of closure to the victim’s family.”
Authorities say Armstrong sold her vehicle in the days after being questioned in Wilson's death.
U.S. Marshals say Armstrong had been signing up for yoga classes using the same alias she flew to Costa Rica under.
According to court records from Travis County, Armstrong will be held on a $3.5 million bond. If she posts that, she'll have to give up her passport and submit to GPS monitoring.