The legendary striker signed for the Reds 50 years ago today (9 July 1962) and recently opened a new exhibition in his honour at the Old Trafford museum to celebrate the anniversary.
Arriving from Torino for a British record fee of £115,000, there was obvious pressure on the Scot's shoulders but he soon started firing the goals that would earn him a place in the club's illustrious hall of fame.
"The Stretford End, as you know, is a very famous part of Manchester United's ground and it always will be," the 72-year-old told ManUtd.com. "It's incredible to think when you play in front of a crowd like that, how it inspires you to do well.
"These guys, particularly in the 1960s, were all working guys who paid good money to see you and want you to do well. You think, 'I've just got to go out and do my best for them because it's their life as well as mine'.
"There was pressure on me as I was a big signing. That type of money was not often bandied about. In today's game, some of them earn that in a week or whatever.
"But I was very fortunate as I knew Sir Matt Busby from being manager of Scotland and obviously manager of Manchester United as well. That was lucky and I was fortunate in that he knew what type of player I was. It was a bit nerve-wracking to begin with but, once I settled in, I felt fine."
Juventus actually tried to sign Law from local rivals Torino but he had his mind firmly set on Old Trafford once Busby declared an interest.