Cutler, 49, will join Van Elle no later than October or earlier if prior agreement can be reached.
Most recently Cutler was managing director of the Balfour Beatty/ Vinci joint venture, with responsibility for the High Speed 2 programme.
From 2010 to 2014 he was chief executive at privately-owned civils contractor Barhale Construction.
Cutler joined Barhale from Morgan Est (2006-2010) where he was managing director. His early career (1990-2006) was at Carillion.
Existing chief executive Fenton will step down for family reasons in two weeks.
Ahead of Cutler’s arrival, Van Elle has engaged Stephen Prendergast, 62, a highly experienced interim manager, in the role.
He has held interim management roles for the last 13 years for ISG, Balfour Beatty, Amey and Network Rail.
Adrian Barden, Chairman, said: “We wish Jon and his family well for the future, and thank him for his contribution to the company over the past eight years, including the successful IPO in 2016.
“We are delighted that Mark is joining Van Elle. He is highly regarded across the industry and will be bringing with him a wealth of valuable experience across all our major sectors, especially in rail and housing where we have many opportunities to build on our already strong market positions.”