The 30-year-old has just returned to action with Blackburn Rovers following a calf injury during his debut for the Championship side.
Despite enduring a frustrating period with injuries in his last two years with Celtic, Mulgrew has been a regular in Strachan’s squad when available for selection.
Mulgrew’s versatility could give the Scots options as they look to close in on the English at the top of Group F.
He won the last of his 24 caps in a 3-0 defeat to France at Stade Saint-Symphorien in Metz in June.
“Charlie Mulgrew has joined the squad ahead of Friday’s match against England,” the Scottish Football Association said in a statement.