In a statement, the FTSE 100-listed firm said Wrigley will stay on as chairman to allow an orderly process while the board seeks a successor.
Meanwhile, the firm’s senior independent director and chairman of its remuneration committee, Jonathan Davie, has also resigned from the board.
Persimmon noted that the two departures relate to its introduction of a long-term incentive plan (LTIP) back in 2012.
It said: “Nicholas and Jonathan recognise that the 2012 LTIP could have included a cap. In recognition of this omission, they have therefore tendered their resignations."
The housebuilder added that the LTIP had been "a significant factor in its outstanding performance over this period", led by a strong executive team.
Persimmon pointed out that since the strategy was launched, it has delivered an increase in the number of new homes supplied of over 65%, invested £2.9bn in new land, returned 485p per share in cash and increased the proposed capital return by 49% to 925p per share, around £2.85bn.
The company said it will now look to appoint a new chairman and will update the market on this in due course.
The group added that Nigel Mills has been appointed its senior independent director with effect from December 14 and he will lead the process of appointing a new chairman.