SAN ANTONIO, Texas (CNN)  -- The three Americans rescued after more than five years in captivity in Colombia say they are doing well but are "overwhelmed with emotion," according to a statement released on their behalf.



"Words alone can never possibly express the thrill and excitement we feel to be back home in the United States of America with our families at our side," the Friday statement from Marc Gonsalves, Thomas Howes and Keith Stansell said.



The Revolutionary Armed Forces of Colombia (FARC) had held the three U.S. government contractors since February 2003, after their plane crashed in a remote region of the South American country.



They were among 15 hostages rescued Wednesday in a Colombian military operation.  Watch Colombians celebrate success »



Also among the rescued hostages was French-Colombian politician Ingrid Betancourt, who returned to France on Friday. She is undergoing medical tests at a Paris military hospital, The Associated Press reported.  Watch Betancourt's joyous return to France »



Shortly after the plane crashed, FARC members killed contractor Tom Janis, according to employer Northrop Grumman, and Colombian army Sgt. Luis Cruz, according to the U.S. State Department.



The three freed Americans are being treated at Brooke Army Medical Center in San Antonio, Texas.  Learn about the former hostages »



"For five-and-a-half long years, we all hoped and prayed this day would come," their statement said. "Now that it has, we're just overwhelmed with emotion. The love and the joy we're all experiencing is beyond description.



"We want to offer our heartfelt thanks to the government and the armed forces of Colombia. The operation they conducted to rescue us was one for the history books -- something we will never forget for the rest of our lives."



Colombian authorities unveiled details and a videotape Friday describing the mission, which involved tricking the leftist rebels into giving up their hostages.  Watch video of the rescue »



Government agents had infiltrated the FARC leadership over several months. This week they talked the rebels into moving the hostages, saying a humanitarian group wanted to check on them.



A helicopter carrying fake rebels picked up the hostages at a rendezvous point, ostensibly to take them to another rebel camp. It actually was a government helicopter, and the hostages were whisked to freedom without a shot being fired.  Learn about FARC »



On Thursday, doctors at the Brooke Army Medical Center said the three Americans appeared to be in good health. Initial tests had for now ruled out the suspicion of infectious diseases, and although other medical tests are pending, "everything really looks well," said Col. Jackie Hayes, a psychiatrist and the lead physician on the men's medical team.



Hayes said patient confidentiality rules prevented him from commenting on reports that Gonsalves was suffering from hepatitis.



Maj. Gen. Keith Huber, commander of U.S. Army South, said the contractors were in the second phase of a three-phase process designed to ease their transition back to normal life.



"They greeted me with a strong handshake and clear eyes and an incredible smile," he said.
Who are the three men? What day were the hostages freed? Who is undergoing medical tests in Paris? Who express gratitude to Colombian military? Where are the men? Who are said to be doing well? Who saved the men?
Marc Gonsalves, Thomas Howes and Keith Stansell Wednesday French-Colombian politician Ingrid Betancourt, Marc Gonsalves, Thomas Howes and Keith Stansell Brooke Army Medical Center The three Americans Colombian military
question: Who are the three men?, answer: Marc Gonsalves, Thomas Howes and Keith Stansell | question: What day were the hostages freed?, answer: Wednesday | question: Who is undergoing medical tests in Paris?, answer: French-Colombian politician Ingrid Betancourt, | question: Who express gratitude to Colombian military?, answer: Marc Gonsalves, Thomas Howes and Keith Stansell | question: Where are the men?, answer: Brooke Army Medical Center | question: Who are said to be doing well?, answer: The three Americans | question: Who saved the men?, answer: Colombian military