The move follows the long-running controversy over his £75m bonus package.
The original figure was £100m but Fairburn agreed to donate £25m to charity following an outcry over his remuneration deal.
Fairburn walked-off a live TV interview with the BBC last month when the issue of his bonus package was raised.
Persimmon said the “distraction around his remuneration continues to have a negative impact on the reputation of the business and consequently on Jeff’s ability to continue in his role.”
Current group managing director David Jenkinson will take over as interim group chief executive on December 31 while the hunt continues for a permanent successor.
Fairburn said: “It has been an honour to lead Persimmon through an exciting period of development.
“I had hoped that revealing my plans to create a charitable trust and to waive a proportion of the award would enable the Company to put the issue behind it.
“However, this has not been the case and so it is clearly now in the best interests of Persimmon that I should step down. I wish the Company the very best for the future.”