Sir Martin Sorrell's marketing services group will publicise the deal at a ceremony involving Sorrell and the Vietnamese Ambassador to London on Wednesday, according to a report in The Sunday Telegraph.
The group will purchase a 30% shareholding in the Vietnam Advertising Company, which is based in Ho Chi Minh City.
WPP saw off competition from its rival Omnicom Group to secure the deal, but it did not give a price in terms of the value of the agreement.
The move is the latest in a series of acquisitions by WPP in emerging markets, where growth far outstrips that of Western markets such as the UK and US, which are predicted to experience small growth in the next few years having reached maturity.
Vietnam, which has a population of 86.1m people, is beginning to generate bigger profits for consumer goods companies such as Pepsico. Anheuser-Busch also announced this week that it was launching its flagship beer brand Budweiser in the country.
Separately, Sorrell is expected to meet David Lowden, the chief executive of the market research firm Taylor Nelson Sofres, this week, in what would be their first meeting since WPP made an almost £1bn bid to buy the company.
WPP could not be reached for comment at the time of writing.