The agency cited a press source from the President’s Office, saying that President Lukashenko signed the corresponding decree on May 25.
It added that the Belarusian government was authorised to sign the agreement with the Vietnamese government, which serves as a basis for further talks.
The EAES agreement was signed by the Presidents from Russia, Kazakhstan and Belarus on May 29, 2014 and took effect on January 1, 2015.
Under the agreement, goods, services, capital and workers can be freely moved among member countries.
The Vietnam-EAES free trade agreement is scheduled to be signed in Kazakhstan on May 29, according to the news agency.
The agreement will be the first the EAES signed with a partner, it added.