Cormier, who has been with the company since 2001, is credited with bringing in the subscription model that has served to make Red Hat the leading enterprise Linux platform.
A statement from Red Hat said Cormier had been behind more than 25 acquisitions that had enabled the company to offer a full modern IT stack.
"When I joined Red Hat, it would have been impossible to predict how Linux and open source would change our world, but they are truly everywhere," said Cormier.
"The opportunity for Red Hat has never been bigger than it is today and I am honoured to lead the company to help our customers solve their challenges and to keep Red Hat at the forefront of innovation."
Whitehurst said: "After working with him closely for more than a decade, I can confidently say that Paul was the natural choice to lead Red Hat.
"Having been the driving force behind Red Hat’s product strategy for nearly two decades, he’s been intimately involved in setting the company’s direction and uniquely understands how to help customers and partners make the most out of their cloud strategy.
"He is a proven leader and his commitment to open source principles and ways of working will enable Red Hat not only to keep pace with the demands of enterprise IT, but also lead the way as emerging technologies break into the mainstream.
Whitehurst is credited with taking the company from one which had US$500 in annual revenue to one that crossed the US$3 billion revenue mark for the 2018-19 financial year.
Apart from being IBM president, Whitehurst will also operate as the chairman of Red Hat, succeeding Arvind Krishna who will now be the chief executive of IBM.
IBM acquired Red Hat for US$34 billion last year, with the deal closing in July 2019.