The US ambassador "communicated officially that Mr Vincent Cooper will not return to Bolivia," Alfredo Rada, a government minister, said.
Philip Goldberg, the US ambassador to Bolivia, said he "greatly regrets" the incident and said Bolivian officials had accepted his explanation.
Cooper, meanwhile, has returned to the US in December and is being investigated by the US state department, the US embassy in La Paz said.
The row erupted after a US student in Bolivia alleged Cooper asked him to pass along information about any Venezuelan and Cuban workers he met in the country.
Alex van Schaick told AP news agency Cooper had said to him: "We know they're out there, we just want to keep tabs on them".
"I was shocked. I mean, this man's asking me to spy for the US government," he told AP.
Venezuela and Cuba are both allies of the Morales government.
ABC News also reported that Cooper made a similar request to 30 new volunteers from the US Peace Corps organisation in July last year.
US officials said in a statement earlier this week that a security adviser at the embassy made an "inappropriate suggestion" to students and volunteers, but said it was "immediately corrected" by another, higher official present at the meeting, AFP reported.
They also said the US does not involve scholars or volunteers in US aid programmes in intelligence gathering.