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Bagust, who joined Breakfast in 2011, made the announcement live on air this morning.
TV One said Bagust had been a regular on New Zealand screens since 1996 and "presented a diverse range of television from live news to talent searches".
Bagust said two years of Breakfast had been "bloody hard work".
"I've loved taking on the challenge of Breakfast, 2011 was the biggest news year in a decade, and it was a privilege going live to the country three hours a morning, keeping Kiwis informed and trying to help make sense of natural disasters like the Christchurch earthquake, Japan's quake and tsunami," Bagust said.
"Two incredible years full of tragedy and triumphs - especially when you add the Royal Wedding, the Rugby World Cup and the Olympics into the mix.
"It's been a rollercoaster ride.
"Breakfast is bloody hard work and it takes a lot of effort from an incredibly committed group of people to make it happen.
"I want to say thanks for having me on the team. Bring on summer and 2013."