It is the board's job to appoint the CEO. There are subcommittees formed to do this, which the existing CEO usually stays away from, because in almost all cases there is a reason the CEO is stepping away/being made to step away in the first place.

Heck even in Steve Jobs' retirement letter (https://www.apple.com/newsroom/2011/08/24Letter-from-Steve-J...) he didn't appoint Tim Cook CEO but rather "strongly recommended" him to the board.