The university joins other facilities named after Mugabe including the government's school of intelligence, a main street in the capital Harare and the highway to his rural home.
"Cabinet has approved the establishment of the Robert Gabriel Mugabe University," Jonathan Moyo, minister of tertiary education, told a news conference.
"There can be no better recognition of President Mugabe's commitment to education and his exemplary leadership."
Moyo said the post-graduate university, to be located in Mazowe, 35km outside Harare, would cost $1bn, but he declined to say how the country would afford to pay the sum.
Mugabe, in power since Zimbabwe's independence from Britain in 1980, will contest elections due next year despite his advanced age and concerns over his frail health.
The country's economic output has halved since 2000, many basic services have collapsed, and government salaries use up more than 90% of all public revenue.
Mugabe has seven earned degrees and 11 honorary degrees, according to state media.
This is a list of universities in Zimbabwe.
- Africa University
- Bindura University of Science Education
- Catholic University in Zimbabwe
- Chinhoyi University of Technology
- Great Zimbabwe University, formerly Masvingo State University
- Gwanda State University
- Harare Institute of Technology
- Lupane State University
- Manicaland University of Science and Technology
- Marondera University of Applied Sciences
- Midlands State University
- National University of Science and Technology, Zimbabwe
- National University of Technology
- Reformed Church University
- Solusi University
- Southern Africa Methodist University
- University of Zimbabwe
- Women's University in Africa
- Zimbabwe Ezekiel Guti University
- Zimbabwe Open University
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