The former Soviet air force officer was arrested on Thursday in a Bangkok hotel hours after arriving in the country on a flight from Moscow.
Bout allegedly thought he was closing a deal with Farc representatives, but it was in fact a sting operation, involving the US Drug Enforcement Agency, Interpol and the Thai police
Thai police believe Bout was planning to negotiate arms deals in Thailand and have said he could be jailed for up to 10 years if found guilty on the charge of procuring weapons for terrorists.
"The US government found out that Bout was planning to use Thailand as a base for conducting illegal arms deals," Thai police lieutenant general Adisorn Nonsee told reporters.
Bout, guarded by heavily armed police commandos, was brought before a news conference in Bangkok on Friday.
He did not speak to reporters but has previously denied US charges against him, insisting he is just a businessman.
Nonsee said Bout had been charged with agreeing to sell weapons to the Farc including surface-to-air missile systems and armour-piercing rocket launchers between November 2007 and last month.
According to the United Nations and the US Treasury Bout's list of alleged customers in Africa includes former dictator Charles Taylor of Liberia, the Libyan leader Moammar Gadhafi, the late dictator Mobutu Sese Seko of Zaire (now known as Congo), and both sides of the Angolan civil war.
Police say they are also searching for an associate of Bout, Andrew Smulian, 46, who faces charges of conspiring to provide material support to a terrorist organisation.
The United States, which has given billions of dollars in military aid to Colombia to support its fight against the Farc, has said it plans to seek both men's extradition.
The Farc has been fighting Colombian government forces for more than four decades, funding its operations through the cocaine trade and kidnapping for ransom.
The group has been designated as a foreign terrorist organization by the US state department.