McGhee was sacked by Bristol Rovers last month, after successful spells at Reading, Leicester and Wolves, where he reached the FA Cup semi-finals.
The 55-year-old also secured promotion with both Millwall and Brighton and then led Motherwell to a third-place finish in his first season in Scottish football.
Although now an assistant as opposed to a number one, McGhee says it is an “honour” to be given the job.
"I am immensely proud and honoured to be asked by Gordon to assist him as national coach,” McGhee told reporters.
"There are few more passionate Scots around that Gordon and I am hugely excited by the challenge of taking our national team up the table in the FIFA World Cup Qualifying group and, hopefully, helping to lead us to the Euro Championships in France in 2016.
"Prior to Gordon's appointment, I had been scouting for Craig Levein so I am aware that we have a very exciting squad of players to work with and I look forward to helping Gordon realise his vision for the national team."
Strachan also admitted his delight at appointing his good friend McGhee. The pair played together for Aberdeen in the early 1980s, and Strachan has said it will be a boost to have him as part of his staff.
"Mark is not just a fantastic coach but a fantastic person,” Strachan added.
"The enthusiasm he brings to the training ground will be a huge asset to me and to the squad.
"It is important that we start out in a positive frame of mind and remind the players that international recognition, as well as being the greatest honour of your career, is also something to savour and enjoy.
"I have known Mark long enough to know that he shares this philosophy and I am delighted to have him on board."