Edwards was the BBC's highest paid news presenter and is a household name in Britain, anchoring the "BBC News at Ten" bulletin for more than two decades
The world's richest person tweeted a picture where he can be seen standing next to the pope, captioning it: "Honored to meet @pontifex yesterday."
Musk's four teenage boys are also pictured, but not his 18-year-old transgender daughter who, on June 20 sought to change her name and sever ties with him. Musk has a total of eight children.
The purpose and location of Musk's meeting with the pope were not immediately clear.
Last month, Musk said there were "still a few unresolved matters" on the deal to buy Twitter, including the number of spam users on the system and the coming together of the debt portion of the deal.