Characterized by dropped "r" sounds, stressed "t" sounds, and soft vowels, the transatlantic accent traces back to linguist William Tilly and his early-20th century World English.
Per "Standard Speech: The Ongoing Debate" by Dudley Knight, World English was not made to reflect any particular country or region. It was meant to reflect class and education.
A person of a certain upbringing could meet anyone of the same background and know they were talking to an equal. Tilly’s teachings became foundational to the transatlantic accent.
Tilly's primary goal with World English was to distinguish the educated and cultured of society. His dialect took root among the upper crust of America's East Coast.
High society members who spoke this way were Franklin Delano Roosevelt and Jackie Kennedy. It was also popular with classically trained American actors in the early 1900s.
Particularly influential among the acting community was Edith Skinner, a disciple of Tilly’s who has been credited with standardizing the transatlantic accent for theater and film.
When cultural mores changed after World War II, the accent dropped in use. The middle-class everyman replaced the highbrow sophisticate as a default character in films.
While the transatlantic accent's popularity has fallen since the 1940s, it hasn’t vanished. It still sees use in mainstream film and television but for comedic effect.