According to the VNA news agency, the ceremony took place in London and involved the ambassadors as the Vietnamese trade minister and high-level officials were unable to visit the UK over the situation with COVID-19.
The agreement will come into force on Friday and stipulates elimination of 99 percent of tariffs within seven years.
"Today our Ambassadors signed the UK Vietnam trade deal securing continuity for businesses", Truss tweeted, adding that the deal will gradually remove 99 percent of tariffs.
Earlier in the month, the country's government announced signing a free trade deal with Singapore and concluded negotiations with Vietnam.
After the UK officially left the EU on January 31 it has been working to secure various bilateral economy-related deals with various countries amid the transition period, which will end this Thursday. Earlier in the day, the UK signed a trade agreement with Turkey.