Finch, 53, is expected to join the Persimmon board and take up the CEO post at the end of the year.
Finch has been the CEO of National Express since 2010, and prior to that, he was group chief executive of Tube Lines and group finance director and group chief operating officer at First Group, where he also held a number of other senior roles.
Roger Devlin, Persimmon's chairman, said: "Dean is a seasoned, well-respected and proven chief executive with an exceptional record. In his current role, he has delivered substantial strategic and operational progress over a sustained period, delivering value for all stakeholders in the business while developing a distinct and cohesive culture, focused on customer care and service.
"The board believes that Dean is a great fit for Persimmon and is well qualified to lead the business into the next phase as we continue to drive a programme of change to become the leading volume builder of good value, quality family homes throughout the UK. I look forward to welcoming him to the company at the end of the year.
"I would also like to thank Dave Jenkinson for his outstanding contribution to Persimmon over many years, and particularly for his decisive leadership during the Covid-19 outbreak. Dave has committed to lead the business until the conclusion of the current financial year in December."
Finch said: "Persimmon is a strong business operating in a sector that has a critical role to play for both the people and the economy of the UK as we emerge from the profound disruption of Covid-19. I look forward to leading the business in its drive to become Britain's best housebuilder and delivering for all stakeholders in the business whilst continuing to deliver strong financial returns to investors."
