The authority has agreed to initially put aside five homes for British citizens who want to leave the country, which has been ravaged by spiralling inflation, food and fuel shortages, and political violence in recent years.
The scheme is part of the Government’s Zimbabwe Resettlement Programme, with which dozens of councils across South East England have been asked to help.
Only those aged over 70, or young people unable to look after themselves without support, are eligible to be rehoused.
A council spokesman said the project would be entirely funded by central government, and that the five homes on offer for those fleeing were difficult to let bedsits and flats in sheltered housing schemes which the authority has otherwise been unable to fill.
The council will receive £3,000 for each property to pay for furniture, £1,500 in resettlement support for each household, along with the prospect of more payments in future, should they be needed.
The Government is now being notified after the council agreed earlier this week to take part, but no timetable has been drawn up yet for when people will start moving in.
Around 3,000 British citizens aged 70 or over, and in need of care, are thought to be currently living in Zimbabwe.
The UK Government has been advising residents to leave the country since 2007, but the resettlement policy was only announced earlier this year.