The act, which states intercourse must be between "a male person and a female person", will be replaced with the word "persons".
According to Virgin Atlantic, LGBT+ discrimination costs up to $4.2 Billion a year in 12 English-speaking Caribbean countries – as much as 5.7% of annual GDP.
Juha Jarvinen, chief commercial officer for Virgin Atlantic, said the move was an "extremely" positive step for Antigua and its people.
"At Virgin Atlantic we believe everyone should be able to be themselves no matter who they are or who they love and we welcome this historic decision to repeal the harmful laws against same-sex intimacy," he added.