Labour and Liberal Democrat leaders Rob Stewart and Chris Holley strongly endorsed the idea at a meeting of full council.
The former Bonymaen RFC captain and Ospreys, Wales and British and Irish Lions player was described as a fine ambassador for Swansea.
Cllr Stewart said he could think of no better person to receive the award. “He has set the bar very high,” he said.
Previous recipients of the honorary freedom of the city and county of Swansea include composer Sir Karl Jenkins, The Welsh Guards, US president Jimmy Carter, and footballers John Charles, Mel Nurse, and Chris Coleman.
Cllr Holley said of the latest recipient, who has 125 Wales caps and nine for the Lions: “There are very, very few players who have achieved what Alun Wyn has done. “It gives me enormous pleasure to second this (proposal).”
A ceremonial council meeting to confer the title on the Wales skipper will take place at a later date.