Fletcher is currently Managing Director of Infrastructure at Morgan Sindall and will take on his new role in December.
Morgan Sindall revealed earlier this month that Fletcher was stepping down from the business after more than three years at the group.
He was previously employed by Lagan Construction Group as Managing Director of Charles Brand Limited between 2000 and 2007.
He then moved to Laing O’Rourke where he held the positions of Managing Director, Ireland and Operations Director, Infrastructure.
Lagan Chief Executive, Kevin Anthony Lagan said: “I am very pleased that Nick has agreed to take on this position.
“Nick brings with him incredibly strong knowledge and experience, which will help him play a key leadership role in Lagan Construction Group’s senior executive team and on the group board.
“It is an additional benefit that, through his previous experience, Nick understands our business and shares our culture and values.”