He will also become the national clinical director for NHS Performance and Improvement, which fulfils the Welsh Government's response to a recommendation made by the Ministerial Advisory Group on NHS Performance and Productivity.
Dr Calvert previously served as medical director and deputy chief executive at Aneurin Bevan University Health Board.
He has also served as National Specialty Advisor for Severe Asthma and led the National Asthma Audit at the Royal College of Physicians.
Health secretary Jeremy Miles said: 'Dr Calvert's experience will prove invaluable to the role of deputy chief medical officer, and he will provide clear clinical leadership from the top in his new role with NHS Performance and Improvement.'
Professor Isabel Oliver, Wales' chief medical officer, added: ‘Dr Calvert will help strengthen medical leadership in Wales and his post will include responsibility for Wales providing clinical leadership to NHS Performance and Improvement and improving our clinical services across the NHS Wales.'
Dr Calvert said: ‘I am honoured to take on this role at such a pivotal time for the NHS in Wales. I look forward to working with colleagues across the NHS and government to build on our shared commitment to high-quality, equitable healthcare for all.'
He will assume his new responsibilities from the beginning of August.