But the £1.5m arrival got off to a poor start with the club he supported as a boy, being substituted in his first starting appearance after conceding a penalty.
Brighton-born Virgo was selected twice by Scotland at B international level.
However, he only made 12 appearances for Celtic, with Strachan sending him out on loan to Coventry and Colchester before the versatile defender's return to Brighton.
Virgo said: "When I knew the club and Micky were interested, it was a very easy decision to make.
"There were other offers on the table, but at this stage of my career I need to be playing regular football and I feel I can achieve that with my hometown club."
Meanwhile, Brighton have also signed a new shirt sponsorship deal with IT specialists IT First.
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