Mr Devlin will step down as chairman of pub operator Marston’s and as the senior independent director of the Football Association on May 1 and start as Persimmon chairman on June 1. He is also chairman designate of bookmaker William Hill.
In December, York-based Persimmon’s former chairman Mr Wrigley and the chairman of the company’s remuneration committee Jonathan Davie quit, recognising their mistake in not putting a cap on the incentive plan.
Nigel Mills - senior independent director at Persimmon, who was appointed acting chairman on an interim basis following Mr Wrigley's departure - said: "Following a very thorough process, the board has agreed that Roger is the right candidate to chair Persimmon.
"I am sure that his wide business experience and his personal qualities will enable him to make a significant contribution to the future of the group."
Last month Persimmon announced another set of stellar results.
The firm is enjoying booming demand for its new homes. The group's underlying pre-tax profit rose 25 per cent to £977m in the year to December 31.
Yorkshire's biggest PLC described the results as outstanding and said the start to the spring sales season in 2018 has been encouraging and private sales are up 7 per cent on last year.
Following the furore over the bonus scheme, directors agreed to forgo around £50m in bonuses last month.
Chief executive Jeff Fairburn's near-£100m award has been cut by £25m following mounting pressure from politicians and some shareholders over the long-term incentive plan introduced by the company six years ago. Angry investors have said the group has been boosted by the Government's Help to Buy scheme.
Mr Fairburn said: "We've listened to what people have said. The executive team have taken various steps to deal with the matter and we came to the conclusion we needed to waive some of the entitlement. I'm pleased it was accepted by the board.
"I've waived 30 per cent of my entitlement and we hope that's supported."
Mr Fairburn plans to donate a sizeable chunk of his award to charity through a private charitable trust.
"I'm sure some of the charities will be Yorkshire-based," he said.
"We very much have Yorkshire at heart. My wife and I are both from Yorkshire."