Scales, who has 14 caps for his country, told Celtic TV he has “grown as a person” since arriving from his homeland.
“I came over, I was raw and didn’t really know what to expect,” he said. “There was a big gap in the level I was coming from and my loan at Aberdeen helped me grow massively as a player.
“As a centre-half, you might peak at a later age than some other positions, so I hope these next four or five years will be my best.
“It is an amazing club and I’ve grown to love it. I love my life here in Scotland and it was good for all parties to get this one.”
Lifelong Celtic fan McCowan, meanwhile, admitted that it “does not feel long” since he was a late deadline-day signing.
“Absolutely buzzing,” he said of his new contract.” Initially I probably wouldn’t have dreamed to have played for Celtic and to get that far.
“To be able to say I’m singing another deal, I feel absolutely electric inside.”
Cowan said it was “a great feeling” to help Celtic win the Scottish title so convincingly in his first season at the Glasgow club.
“The highs have been amazing and hopefully there’s more of that,” he said.
“I have just became a lot more mature. It has been great to learn from these guys who have been here so long.”
Martin O’Neill praised both players during his two spells as interim manager this season.
Of Scales, he said: “I don’t know what he was like for the first part of the season. But, since I’ve been here, he’s been absolutely terrific.
“We are a better team when he’s in and he’s also got the ability to play at left-back. He’s been a major player for us this season.”
Meanwhile, O’Neill said McCowan had made “a major contribution” and added: “He’s a solid little midfield player with a good eye for a pass and, if close to goal, you feel he is going to go close to the target.”