Johnson's contribution to the company was recognised recently with her being named a finalist in the executive of the year category in the Deloitte Top 200 Awards.
IAG Group managing director and chief executive Peter Harmer paid tribute to the outgoing executive.
"Jacki is an exceptional leader," Harmer said. "The reasons she'll be missed in New Zealand are why she has so much to offer within the new group leadership structure."
Ms Johnson's new role as IAG Group Executive, People, Performance & Reputation will see her responsible for people and culture, corporate affairs, shared value and the IAG Foundation.
"If IAG is to maintain a sustainable competitive advantage in the markets it operates in, we need to have high-performing and engaged people and a strong reputation with all our stakeholders including our people, government and communities," Johnson said. "I'm excited to be taking on this responsibility."
Olsen has had a lot of experience with the company, including being in charge of the integration of AMI into IAG following its acquisition in 2012. He will take over as New Zealand chief executive on January 1 2016, subject to approval from the Reserve Bank.