Miller, aged 43, was previously chief financial officer of GMG and was named as incoming interim CEO on 23 April (assumed once McCall had left the group).
McCall's decision to leave the publishing group was revealed on 23 March and she left last month.
Miller assumes the permanent position at the helm of the group behind The Guardian and The Observer, with immediate effect.
Amelia Fawcett, chair of GMG, said: "Andrew is the ideal appointment to this role, following a rigorous recruitment process that produced a very high-quality shortlist of candidates.
"He has great financial acumen, an intimate understanding of GMG’s portfolio and a full appreciation of our unique purpose and values.
"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."
GMG posted pre-tax losses of £171m for its full financial year to 28 March, after double-digit falls in adspend and impairments following investments in Emap and GMG Radio.