Before accepting his new position, Crockett was the company's deputy chairman and was a board member for four years.
He will be replacing Ellvena Graham, who served as the chairman for four years.
Crockett has previously served as the founding CEO of the Digital Catapult innovation centres and was the chief digital officer at Rolls-Royce.
Neil Crockett said: "Having been involved in the local innovation ecosystem for over a decade, I’m delighted to be taking over as chairman of Catalyst at this exciting, pivotal time in its evolution. I would like to thank Ellvena for the fantastic job she has done in guiding Catalyst and leading the board.
Outgoing chairman Ellvena Graham added: "I have thoroughly enjoyed my time at Catalyst and am very proud of what has been achieved during my tenure, including the launch of our inclusive innovation strategy, the Stryve and Role Models programmes, and the launch of our new goals to 2035.
"I wish Neil the very best as he leads the Catalyst board into an important new phase for the organisation. He has a rich mix of global and UK business operational experience and skills which will no doubt be invaluable to Catalyst as it enters this new chapter."