Bournemouth Borough Council's cabinet agreed to buy property in a bid to save money on bed and breakfast accommodation.
A spokeswoman said the council hoped to make its first acquisitions by the end of the summer.
The authority said it expected to buy about 60 properties over three years at a cost of Â£10m.
The plan also includes the purchase of more rental properties for the council's own social housing stock.
Housing councillor Robert Lawton said, by owning the properties, the council could ensure they were of "good quality and well managed".
Also, any income generated or increase in property values would come back to the council, he said.
The scheme would be funded using a combination of council funding and a loan.
A council has agreed to set up a private sector landlord company so it can rent directly to homeless people.