The Motherwell manager will combine his club duties with a role under Strachan and assistant manager Mark McGhee, as the new team begin their roles in a Pittodrie friendly against Estonia on February 6.
McCall joked he was paying tribute to one of his Scotland heroes, Joe Jordan, after knocking out a front tooth while biting a mint this morning, adding: "It's something I really want to smile about and can't."
But there was no disguising his delight at being recruited by Strachan.
The England-based manager revealed McCall would help monitor players in the Scottish game but also praised his "inspirational qualities".
Leeds-born McCall, who won 40 Scotland caps, said: "I'm absolutely honoured to be asked along to be part of the national set-up and also with it being Gordon asking me, I'm just really honoured and proud.
"Anyone who knows me, other than my accent, I'm 100 per cent committed to Scotland.
"I played against Gordon and came across him but I don't really know him that well, the same with Mark, but we had a good relaxed chat when we met up on Monday night.
"I never thought in my wildest dreams I would be anywhere near the national set-up and it came out of the blue."
When asked what he would bring to the role, which was vacated by his Fir Park assistant, Kenny Black, when Craig Levein lost his jobs, McCall said: "I don't know, I am what I am. I'm enthusiastic and passionate, certainly about my football and especially anything to do with Scotland.
"I'm thrilled to be given the opportunity to work with good players and to be involved in the set-up.
"And not only that, to work under both Gordon and Mark, who are both experienced managers and coaches, it will benefit myself, and seeing good players up close, even the opposition as well.
"We'll see how it goes but obviously I've spoken to Kenny Black, my assistant at Motherwell. One or two of the staff are giving me stick for coming in and taking his job.
"I used to actually be quite envious of Kenny when he went away with Scotland - because he was coming away with Scotland and it left me with the rest of the lads at Motherwell, which was hard work.
"But he is pleased for me as well and I think it will be a similar role."
Strachan turned to one of his closest friends, McGhee, a former Aberdeen team-mate, when selecting an assistant but he has not had a working relationship with McCall.
However, the Scotland manager was gushing in his praise for the former Rangers and Everton midfielder.
Strachan said: "In many ways Stuart typified the classic Scotland international player: he was passionate and combative but he was also hugely influential and inspirational.
"He has done a tremendous job at Motherwell and his knowledge of the game, and especially his knowledge of the Scottish scene, will be invaluable."
Strachan and McGhee have both worked in Scotland in recent years but can utilise McCall's working knowledge of the Clydesdale Bank Premier League.
"It's funny because we used to give Kenny a bit of stick for not getting Jamie Murphy and even Keith Lasley at 73, or whatever age he is, into the squad," McCall said. "Now the lads will be trying a little bit harder in training.
"Obviously Gordon and Mark have got a good knowledge of what's going on down south. Mark was doing some scouting for Scotland anyway and Gordon sees a lot of games with his TV work, and I see the players up close on a regular basis.
"In the last game we had Murray Davidson and Andy Shinnie making their debuts.
"We have got good players, the majority in the middle to front area, I'm sure Gordon will be trying to get as many players as we can together and get them in a system and formula that can get us a winning run.
"Once you get a bit of momentum, hopefully everyone buys into it."
Meanwhile, McCall insisted his new role would not impinge on his Fir Park duties.
The 48-year-old, who has led Motherwell to the Scottish Cup final and Champions League qualifiers in his two years in charge, said: "I don't see it being a problem. When Kenny used to go away, normally the league clubs have a couple of days off to recharge the batteries when it's international week.
"The worst that can happen, say for example the Estonia game is on a Wednesday night, I'll be back in the office first thing on Thursday morning.
"Thursday is the earliest, and it's probably Friday, that you look to shape up teams even for the Saturday opponents.
"There won't be any conflict whatsoever. I think it can only be beneficial as well."