Mays has been in the role at RES since its formation in 1981 and guided the company to become an all-round wind-industry player.
RES has its fingers in many pies, ranging from long-range transmission lines in the US to offshore wind developments in French waters.
Mays' contribution to wind power, which includes a spell as president of the European Wind Energy Association between 1994 and 1999, was recognised in 2010 when he was awarded the Poul la Cour prize for outstanding achievement in the field of wind energy.
He regularly featured in Windpower Monthly's Top 30 influencial people, and was placed 25th in last year's poll.
"I feel truly privileged to have led the amazing and dedicated team at RES to create the highly respected international business we have today. Who would have thought, when we founded the company all those years ago, that we would build a business employing over 1,500 people across 13 countries with a revenue topping one billion pounds?" said Mays.
Mays will continue in the role until the end of the company's financial year, 31 October 2016. Ivor Catto, formerly CEO of infrastructure advisory firm Hyder Consulting, will replace him. Catto will join RES from 3 May as deputy CEO for a handover period.
Mays will continue as a non-executive director on the company's supervisory board.