The Latin-based script was developed by the Portuguese and subsequently used by Jesuit missionaries. Its usage continued during the French colonial era, and eventually supplanted the Chinese writing system in Vietnam. More so than any other nation in East Asia, Vietnam was under strong European influence, which aided the adoption of the Latin script heavily extended with diacritics, mostly to denote the tonal nature of Vietnamese, which cannot easily be denoted in a "standard" Latin alphabet.

For sources, you can have a look at Keith W. Taylor's A History of the Vietnamese or at McLeod and Nguyen, Culture and Customs of Vietnam.