Most are on National Diploma courses equivalent to A-level and national vocational qualifications level four, in subjects identified as essential for the economic development of the former British colony. The main courses are in subjects such as mechanical engineering, fashion design, computer studies, electronics, business and finance.
The initiative piloted in Leeds will be launched nationally in the city tomorrow. It is led by the Zimbabwe Educational Trust which elicited support from the 33 colleges.
Its director, Vulie Mkandla, said: "There are many young people in Zimbabwe who do very well and achieve excellent grades in secondary education but then face a bottleneck in further education."
Zimbabwe has become one of the major exporters of students to the UK as it struggles to build up its own FE sector.
There are only a few colleges and universities in Zimbabwe and the costs of courses tend to be out of reach of the majority of families.
Ms Mkandla approached British colleges and universities asking them to help, and found that many were prepared to waive fees.
"We tried the scheme first in Leeds and it has now mushroomed to involve colleges around the country," said Ms Mkandla.
The colleges are effectively providing a bursary scheme for the students. They cannot claim any cash for the students from the further and higher education councils. The lower fees, however, do not require significant cuts since the extra students bring only marginal costs.
Airedale and Wharfedale College in Leeds has already accepted several Zimbabwean students. The principal, Chris Pratt, said: "This is more than an academic exercise," he said. "I am sure all our students have benefited from the experience of sharing their studies with students from a background as culturally diverse as Zimbabwe."