Government to prosecute agents as Colombia denies espionage allegations.
Chavez accuses the US of backing a 2002 coup attempt against him.
Bolivia and Nicaragua have also opposed the deal, for which the US has earmarked $46m, mostly to refurbish the Paleanquero air force base near Bogota.
But, after voicing initial resistance Inacio Lula de Silva, the president of Brazil, came round to supporting the pact following explanations from US officials.
Colombia is the world’s biggest producer of cocaine – the fight against which Washington has contributed $6bn over the last nine years.
The pact marks the move of the US’s anti-narcotics hub from Manta in Ecuador after Rafael Correa, the country’s leader and Chavez’s ally, refused to allow an increase in the US’s presence in his nation.
Washington and Bogota said that the agreement would not lead to any breaking of the current limit of 800 military and 600 civilian contractors established by US law.
Some Colombians have criticised the decision to maintain diplomatic immunity from prosecution for US personnel in Colombia.
Ana Duque, the US embassy spokesman, said that the agreement’s text would be released in the US Federal Record within about a month.