"Thank you today to the Aberdeen City Council and the Denis Law Legacy Trust for this unbelievable moment."
Law, named affectionately The King, unveiled the statue, featuring his finger pointing to the heavens and dedicated with the single word "Legend".
Sir Alex said: "I think this statue definitely captures him - the only thing is I don't see him wiping his sweater on his nose.
"It is an honour for me to speak by this wonderful statue in the city of Aberdeen.
"I think Denis epitomises a Scotsman, he showed fantastic courage at 15 years of age, to go down to Huddersfield, as a young kid, not many have the courage to do that type of thing.
"He had the chance to be a great player, he took the chance and his career was incredible. He was a fantastic player. He was the greatest Scots player of all time, no question."
Law added: "The city and people of Aberdeen have always meant so much to me and this is truly a great honour.
"To be joined by so many of my family and friends, including Sir Alex, just makes it all the more special.
"I would like to thank them all for joining me today and also to Aberdeen City Council and Denis Law Legacy Trust for this fantastic tribute which goes way beyond my wildest dreams."
The statue with an overall height of 4.7 metres and the bronze of 2.7 metres is sited at the gable end of Provost Skene's House, which recently reopened as a new visitor attraction after the city council's £3.8 million renovation.
It was sculpted by Alan Herriot, who was also commissioned by the council to create the statue of King Robert the Bruce outside nearby Marischal College.
Law, 81, was born and raised in the Printfield area of Aberdeen.
The former European footballer of the year and Scotland's only winner of a Ballon d'Or went to Powis Academy, before moving to England to play for Huddersfield.
Mr Crockett said: "The people of Aberdeen hold Denis Law very close to their hearts and this statue represents appreciation of a local lad done good.
"Denis is a remarkable man, not only for his outstanding achievements on the football pitch for clubs and country, but for the fantastic charity work he has done over the decades especially through the Denis Law Legacy Trust.
"Located in the heart of the city centre I am sure thousands of people - young and older - will come and take a photo alongside this magnificent statue of The Legend that is Denis Law."