Coldwell was at the helm of Pagoda for almost 20 years, including as MD for 15 years and more recently as chair.
With Sir Michael Hirst, he bought PS Communications in 2000, which was later rebranded as Pagoda.
The CIPR fellow was known for his contribution to the industry on issues including ethics and standards.
Pagoda said Coldwell had 'a rigorous approach and strong intellect' and was 'hugely respected throughout the PR and public affairs industry and by the many people who had the privilege to work with him over his long career'.
"We are completely heartbroken to lose such a respected and loved colleague," said Pagoda MD Angela Casey. "Working with Ian was a joy. He always took the time to encourage all colleagues with guidance and advice, while bringing sage counsel to the many organisations he worked with.
"The loss goes far beyond our team and many people will miss Ian and will remember him fondly. He worked tirelessly, even when seriously ill and against everyone’s advice, but he loved his work, and he did it well."
Coldwell, a keen sailor, worked as PR and community manager for Centrica in the mid-to-late '90s and had PR stints at Edinburgh City Council and London Borough of Ealing Council earlier in his career.
He leaves behind his wife, Jackie Brock, and two children, Tara and Corin.