The full back, part of the Rangers team which won the European Cup Winners’ Cup in 1972, died on Thursday after losing his 18-month battle with cancer.
But Greig - like Jardine born in Edinburgh but a hero to the Ibrox support - hailed a man he has known for over half a century.
Greig - who was Jardine’s skipper as he led the club to their only European title when they beat Dynamo Moscow in Barcelona almost 42 years ago - said: “I have known for quite a while how ill Sandy has been and how hard he has fought. Unfortunately it was one battle he was not able to win.
“But irrespective of the fact I knew how ill he was, the news on Thursday night still came as a big, big shock.
“Sandy never failed to impress people when he met them. People should remember him as an excellent football player and a gentleman. For me, above all that, I will look back on him as an old and trusted friend to me.
“I first met Sandy 50 years ago and we travelled back and forward from Edinburgh to Glasgow on the train for years.
“We lived round the corner from each other and our kids grew up knowing each other. In many ways, he was like my little brother. I will never forget him.”
The coalition group the Union of Fans has called off a demonstration against the unpopular Rangers board planned for Saturday’s final home match of the season against Stranraer out of respect to Jardine.
Derek Johnstone, another former ‘Barcelona Bear’, told Radio Clyde: “People talk about legends these days but that word is bandied about far, far too easily.
“But Sandy Jardine was a Rangers legend. There will be many, many Rangers fans deeply saddened by this news.”
Hearts manager Gary Locke hailed Jardine as a Tynecastle legend for his central role in one of the club’s greatest teams.
Jardine spent six years at his boyhood heroes, the latter two as co-manager with former Rangers team-mate Alex MacDonald, and made more than 200 appearances.
The Edinburgh-born defender almost helped Hearts to the double in the 1985-86 season but they lost their last two games of the campaign against Dundee at Dens Park and Aberdeen at Hampden to leave a Scottish Football Writers’ Player of the Year trophy as mere consolation.
Locke said: “I grew up watching him in the ‘86 team. It’s really sad news and everyone at Heart of Midlothian sends their condolences to his family and everyone at Rangers as well.
“Obviously I trained here as a kid and Sandy was assistant manager but I watched that team religiously and went everywhere. He played a huge part in the success that season.
“They were a fantastic team to watch, they just came up a little bit short at the end. Sandy played a huge part in bringing through the likes of Craig Levein, John Robertson, Gary Mackay, all these players.
“I was a bit young to see him in his playing days at Rangers but at Hearts he was a fantastic player and the way he went about everything too.
“When we played Rangers at Ibrox we would see him before the game and after the game and he was a fantastic person. He is a huge loss to Scottish football.”
Current Rangers boss Ally McCoist dubbed Jardine a “great man” while former Manchester United boss Sir Alex Ferguson - another former Ibrox team-mate - said: “Sandy was a noble and courageous man. The respect he is held in at Rangers is immense.
“He was one of the greatest players ever to wear the jersey. To Shona and family, we express our sympathy and sadness.”
Jardine is survived by his wife Shona, children Steven and Nicola as well as several grandchildren.