She starts on Monday, working across a client portfolio spanning multiple sectors.
Before joining BT, Cleevely spent over a decade working in international PR agencies including GolinHarris and Charles Barker. She has provided comms consultancy for clients such as EMC, IBM, Oracle and SAS Institute.
Hudson Sandler MD Kirsty Leighton, who worked with Cleevely at Weber Shandwick, said: "Her expertise across broader marketing and customer engagement gained from seven years at BT, leading corporate relations programmes for BT Business and marketing for BT Wi-fi, along with her deep understanding of storytelling and campaign planning from 10 years agency side, will enable her to make a valuable contribution as we support our clients in a rapidly changing communications environment."
Cleevely said: "This is a great time to be joining one of the City's most respected communications brands."
She is the latest director appointment for Hudson Sandler as it targets expansion, including the recent opening of an office in Hong Kong.
Last month the agency announced it had appointed Alex Clelland, formerly EMEA head of corporate comms for global investing banking and financial services group Macquarie, as a director in its financial services team.