Swift, 34, also became the most-streamed artist in a single day on the platform when her record was released on April 19, according to the streaming service.
The company wrote on X: "History made! On April 19, 2024, Taylor Swift's THE TORTURED POETS DEPARTMENT was the first album in Spotify history to have over 300M streams in a single day."
It comes after Swift became the first female artist on Spotify to reach 100 million monthly listeners in August 2023.
The Grammy winner's highly anticipated 11th studio album includes collaborations with Florence And The Machine and Post Malone and her song titles and lyrics appear to make reference to some of her former flames.
Fortnight, featuring American rapper and singer Post Malone, is Swift's first single from the album and has become Spotify's most streamed song in a single day.
Her music video for the track includes an appearance from Dead Poets Society stars Ethan Hawke and Josh Charles, as well as her collaborator Post Malone.
Hours after dropping the 16-song edition of her album the US pop superstar announced an expanded version with an extra 15 songs, titled The Anthology.
With AAP.