Lester will replace as Philip Cox who stands down as chairman on 1 January 2020.
He joins as Kier battles to reduce its debt with plans to find buyers for its property and housebuilding businesses.
He brings extensive experience of finance having been at the Royal Mail Group from 2010 to 2017.
Prior to that, he was Group Finance Director of ICAP plc from 2006 to 2010, and has held a range of senior finance roles at Diageo, including Group Financial Controller and Group Treasurer.
Lester is a chartered accountant, qualifying with Arthur Andersen before spending the early part of his career with Kleinwort Benson.
More recently, he has been a non-executive director of Man Group, Barclays, where he stands down on 1 January, and Capita.
Lester said: “I am delighted to be joining Kier as its Chairman. I look forward to working with the board to deliver the group’s strategic priorities and in continuing to build the foundations for its future.”