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Board of trustees chairman Richard Wingham said Mr McIvor would take over leadership of the school at the start of term 3.
Mr Reddiex left the school last week to become the rector at Dilworth School in Auckland.
Former Wellington College headmaster Roger Moses will be the acting rector in term 2.
Mr Wingham said the board was impressed with the calibre of applications for the permanent role and was delighted to secure Mr McIvor as the new rector.
He said Mr McIvor had been the rector of Timaru Boys' High School for the past five years, and had led the school through a period of change and consolidation, positioning it for continued success.
"With 24 years of experience in education - 16 of these specialising in boys' education - Mr McIvor has demonstrated a passion for boys' education and a clear understanding of the King's culture of personal excellence.
"Mr McIvor brings significant boys' school experience, combined with traditional values that are essential in maintaining the culture and high performance of the school.
"We look forward to Mr McIvor's arrival for term 3.''
Timaru Boys' High School chairman Peter Stayt said the school was sad to see Mr McIvor depart, and had nothing but praise for his contribution to the school.
"The school is in great heart and in a stronger position than when he joined us, and we believe that the foundation has been well laid for the school's future.''