The 31-year-old forward replaced Hugo Lloris as Spurs captain this summer, with England skipper Harry Kane having left to join Bayern Munich.
Son rose to prominence under Pochettino in north London, developing into one of the world’s best attackers as the pair built a close personal relationship.
Pochettino spoke about Son’s new leadership role as Chelsea attempted to stop him at the Tottenham Hotspur Stadium on Monday night.
“He’s a great professional, a great player, I’m so happy he’s the captain,” Pochettino told reporters. “People grow, people become more mature, and they are top of the table so he must be doing something good as captain.
“When people you like and love are happy and doing well, that increases your personal happiness. We are this type of people that love and enjoy when people we know and you are part of his life are doing well.”
Some believe Tottenham have improved without Kane, who was sold for close to £100million this summer.
Kane is the top scorer in Europe’s top-five leagues with 17 goals in 14 matches, but Spurs have made their best start to a Premier League season ever in his absence.
Pochettino does not subscribe to the view that Spurs are better without the striker he helped build, adding: “Harry Kane is one of the best strikers in the world and for sure Tottenham is missing him but at the same time they are performing really well.
“They have found a way to perform and be at the top of the table, a better position is impossible.
“You can’t compare things you cannot prove because today with Harry Kane instead of being one point clear at the top they could be by 10 points clear. Or maybe they would not be performing well. It’s difficult in football to confirm something like this.”