It is understood Garner regularly starts works at 4am, well before the show screens from 6am on weekdays.
Garner said he would miss working with co-hosts Mark Richardson and Amanda Gillies.
"I have a particularly heavy heart leaving our AM team and have loved being on air daily with Amanda and Mark. They are brilliant, fun co-hosts and I trust them immensely.
"This place has been home for 20 years and it's bloody hard to say goodbye but I have to. I have a few important family and personal things that need my attention and now is the right time to go.
Duncan Garner has hosted the show since 2017.
"And of course, thanks to our loyal audience. You are smart, savvy and opinionated. Thank you for your kind wishes over the years. I will miss you," Garner said.
"I am so proud of what we have achieved in all the teams I've been a part of and in this tough, hostile business you're deluded if you think you do it alone.
"Three and now Discovery has the most talented staff and best journos I've ever worked with. Their commitment, knowledge, sources, sheer guts and work ethic is legendary and continues to be so."
Focus on 'personal and family matters'
An email sent to Three staff from Newshub's director of news Sarah Bristow: "After 20 years with Three, Duncan Garner has made the difficult decision to resign in order to focus his attention on some personal and family matters.
"Morning television hours are gruelling and I respect Duncan's decision and wish him the very best for the future."
Bristow said an announcement would be made regarding Garner's replacement in due course.
Garner is an award-winning journalist who worked as Newshub's political editor and later hosted Radio Live's Drive show.
