Bradford-based Redfern, which has a turnover of almost £300m, rebranded last year as it looks to move beyond its core public sector client base.
"Redfern is a tremendously impressive company that has seen sales growth of nearly 500 per cent in the past three years," said Cream director Elizabeth Hudson.
"The company has a superb reputation within the public sector and we aim to strategically build on this success to bring the benefits of using Redfern to more clients in the private sector."
Cream, which is based in Barnsley, was approached by Redfern for the retained brief and there was no competitive pitch.
Redfern CEO Mark Bowers said: "We were impressed by Cream’s ability to quickly grasp what Redfern is all about and what we’re hoping to achieve in the coming months."