Colgan joins as goalkeeper coach from Wigan Athletic while Reid joins as first-team coach.
Colgan, a former Republic of Ireland international, enjoyed a playing career spanning over 20 years, featuring for several teams including Chelsea, Hibernian, Barnsley and Grimsby Town and playing over 300 first-team matches.
The 47-year-old took on a coaching role at Huddersfield Town, firstly in the academy then with the first team, before joining Wigan in 2017 and now moves to The City Ground.
Reid takes up the role of first-team coach, combining his role at Nottingham Forest with a coaching position with the Scottish FA as part of their senior set-up.
An experienced player with over 350 career appearances to his name, Reid featured for the likes of Millwall, Blackburn and West Brom, as well as playing 23 times for the Republic of Ireland.
As a coach, the 39-year-old has worked for Reading, Crystal Palace and West Brom and now joins as part of Chris Hughton’s backroom staff.