It's just that he is First Secretary Of State, as well as being Foreign Secretary. It's the first bit that puts him in charge rather the the latter.
Hague also had that position when he was foreign secretary, but Damien Green held the role under May, and Osborne had the position post-2015 for Cameron. Mandelson had it for a bit at the end of the Blair years.
Normally it's combined with Deputy PM. Hestletine had both roles under Major and Prescott had both under Blair.