He takes over from Carolyn McCall, who left GMG at the end of June to take up the position of chief executive at easyJet.
Miller, who was previously the chief financial officer of GMG, was placed in the role of interim CEO last month, but has now had his permanent status confirmed.
"It is a great privilege and responsibility to lead Guardian Media Group and to play a key role in supporting the independence of our journalism," Miller says in a release. "While the media sector faces continued change, to which we will need to adapt, our strong portfolio of businesses and investments means we have a solid base from which to move forward."
Amelia Fawcett, chair of GMG, says Miller is "ideal" for the role.
"He has great financial acumen, an intimate understanding of GMG's portfolio and a full appreciation of our unique purpose and values," she says in a release. "He knows how to drive successful digital transformation and has led large-scale financial transactions. Most importantly, he has the ability, desire and vision to lead GMG through the next stage of its development and to ensure a sustainable future for our journalism."