The borough council said the tests will be carried out over the next year at Iford Meadows, Millhams Mead, Kings Park and Turbary Common.
It said there is no evidence the gases being emitted at the former waste burial sites are a cause for concern.
A number of small standpipes will be placed into the ground on council-owned land and in nearby residents' gardens.
"When the results are available we will decide if we need to take any further action"
The work will start at the end of October and be carried out by a team from Bournemouth University who will analyse the gases every two weeks.
Councillor Jean Moore said: "We know that when materials tipped in a landfill site break down they produce a mixture of gases.
"At the moment there is no evidence that the gases being given off are a cause for concern. We are now making further investigations to find out if there could be a problem in the future.
"When the results are available we will decide if we need to take any further action."
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