He had been seeking stability, having never spent longer than two seasons at his previous clubs, which included Bayern Munich, Fiorentina and Milan. Then, in 1994 he moved to Glasgow.
"About two or three months after I'd signed for Rangers, my agent phoned to say: 'Barcelona want to buy you,' said the man who was also a European Championship winner with Denmark in 1992.
"But I said: 'no chance,' and went to tell [manager] Walter Smith I wanted to stay at Ibrox for several years.
"He looked me in the eye and said: 'So you would rather play Falkirk on a Tuesday night than join Barca?'" Yes, came the reply and that was it.
And what a brilliant decision it was because, in four years at the club, Laudrup was part of the squad that won nine successive league titles, equalling their city rivals' long standing record.
"I was told about Celtic's nine-in-a-row," he explained to the BBC. "Strangers would tell me. They said that if I could be part of that I'd be immortalised. The day we did it I remember Richard Gough crying. At that point I fully realised what it meant to people."