Moyo spent three weeks in jail last year accused of obtaining fake accreditation documents for two of the US newspaper's journalists on a visit.
The New York Times says the charges were baseless and that a Zimbabwe Media Commission official had issued him papers for Christina Goldbaum and Joao Silva. They were expelled.
"It was a nasty experience, sleeping on the concrete floor and having no contact with my family," Moyo told Reuters. "It was terrible, but I'm optimistic that things will go well."
Officials were not immediately available to comment on the trial due to take place at a court in Bulawayo, Zimbabwe's second biggest city. But a spokesperson last year accused Moyo of paying a bribe to break immigration laws.
The government of Mnangagwa, who replaced long-serving autocrat Robert Mugabe in a 2017 coup, has testy relations with non-state media. Another prominent reporter, Hopewell Chin'ono, who is critical of the government, has been arrested three times.
"The state has a very weak case ... Jeffrey believed he was dealing with a bona fide official of the Zimbabwe Media Commission," Moyo's lawyer Doug Coltart told Reuters.
Moyo had also worked for the Thomson Reuters Foundation charity.
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