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She takes over from Sally Buck who resigned as chairwoman at an emergency meeting last week.
Buck stepped down from the role, which she has held for the past four and a half years, due to ill health.
She will remain a board member and still sits on the Canterbury District Health Board. Buck was a Christchurch city councillor for 15 years.
Davids was deputy chairwoman of the board before replacing Buck and has been a member for three terms.