Chiwenga replaces Obaddiah Moyo who was removed from the post last month after allegations of corruption.
In his new role, Chiwenga will be required to "stabilise, restructure and reform" the national healthcare system, the government said in a statement.
The main opposition Movement for Democratic Change (MDC)immediately criticised the appointment, saying Chiwenga was not the right man for the job in a time of the coronavirus pandemic.
Zimbabwe has recorded more than 4,000 COVID-19 cases and 80 deaths and health officials say infections will continue to rise for sometime.
The MDC said in appointing Chiwenga, Mnangagwa had shown a "gross display of incompetence."
Chiwenga spent four months in China receiving medical treatment for an unknown illness until November last year. He has returned three times since then for medical check-ups, according to government officials. (Reporting by MacDonald Dzirutwe Editing by Promit Mukherjee and Tom Brown)
epa06915639 ZANU-PF Deputy President Constantino Chiwenga (L) and President Emmerson Mnangagwa (R) raise their fists at the National Stadium, Harare, Zimbabwe, 28 July 2018. Reports state that there are 23 presidential candidiates and more than 120 parties who have registered to take part in the elections as Zimbabweans go to the polls on 30 July 2018. EPA-EFE/YESHIEL PANCHIA 