The Daily Mail says Ziyech hopped on private jet bound for London with his entourage on Friday evening.
Ziyech agreed his £40million move to Chelsea in February but coronavirus restrictions have delayed his arrival at the club.
He officially became a Chelsea player on July 1 but is is only now that he is joining up with his new team-mates.
Speaking earlier this month, Frank Lampard revealed: "We are waiting on quarantine news to make sure they can travel, move around and work as we'll need them to."
But reports suggest Ziyech is now joining up with his new colleagues, though he isn't eligible to feature until next season.