"My name's Elba, Idris Elba," he captioned a selfie, referencing the character's signature introduction, "Bond, James Bond."
As the tweet made headlines, he returned to his feed and posted, "Don't believe the HYPE..."
Craig, 50, previously played the globe-trotting hero in Casino Royale, Quantum of Solace, Skyfall and Spectre.
His successor has not been named yet.
Elba, 45, is best known for his work on the television dramas Luther and The Wire, as well as in the films Molly's Game, The Jungle Book, Thor, Pacific Rim, Zootopia and Mandela: Long Walk to Freedom.
my name's Elba, Idris Elba. pic.twitter.com/kEyyaVg8JX- Idris Elba (@idriselba) August 12, 2018