Mr Mundry has been a member of the cabinet since 2015, holding the portfolio for transport, highways and public realm.
He is also a youth worker and represents Warrington on various bodies including the Transport for the North board and the Cheshire and Warrington Local Transport Body.
Mr Mundry said he had “strong ambitions” for the town.
“I want us to build on our strengths as a well-connected, business-friendly economic leader.
“To drive ahead with our net zero ambitions and to work with partners to improve the health and wellbeing of our residents, particularly the most vulnerable.”
Ms Henshaw has been named as deputy leader following the departure of Cathy Mitchell.
She has held a cabinet role since 2022 and is currently a solicitor at Citizens Advice.
She previously worked as a nurse and a social worker.
