Touching on the attraction of Celtic, he revealed: "The size of the support, the tradition, the history, all the things I hold true when I talk about footballing philosophies.
"I will try to put my stamp on the team and try to give the supporters something back."
Celtic chairman John Reid suggested that Mowbray was the natural choice as Strachan's successor.
"Welcome back Tony and, in a very real sense, welcome home," he said.
"Because that's how the Celtic supporters and the wider Celtic family feel. We're absolutely delighted to have secured Tony Mowbray as our manager.
"Tony's career speaks for itself; here and elsewhere as a player and a manager.
"The reason he is here today is because it was our firm view that he's not only shown he can bring football success with flair but he's also shown character, strength and determination."
Reid thought that Mowbray could revive Celtic's fortunes after losing the SPL title to Rangers.
"We've had a degree of success in recent years, but we had a disappointment three weeks and three days ago," he said.
"The fightback starts here and there's nobody better to lead that than Tony."
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