Cotterill watched the Swans 1-0 victory over Derby County at the Liberty on Friday night and is reported to have signed on loan until January with a three year deal to follow.
He is also expected to be within the matchday squad for Saturday’s trip to Newcastle in line to make his debut for his new side.
The former Bristol City, Wigan and Sheffield United man told News of the World “I’m glad to get away from Sheffield United.
“I’ve played against Swansea a few times and watched them against Derby on Friday night. They play great football.
“A few clubs were interested but I’ve made the right decision.”