In a statement, the Premier League said: "Following media disclosures earlier this week and discussions with David Pemsel, the Premier League has today accepted David's resignation and he will no longer be joining as chief executive.
"Richard Masters will continue as interim chief executive.
"No further comment will be made at this stage."
There has been no reason from Mr Pemsel as to why he has decided to stand down.
He was appointed last month and was due to start at the role at the end of February after serving his notice at the Guardian Media Group.
At the time the chairman of Chelsea, Bruce Buck, praised Mr Pemsel's "straightforward style and personal integrity".
The company's long serving chief Richard Scudamore announced that he was going to stand down in June 2018, but the position now remains vacant, after three people have now turned the job down.
Susanna Dinnage was Premier League's first choice last November but later pulled out, saying she had a change of heart.
It was reported that Tim Davie, the head of BBC Studios, also turned down the job.