“I loved all of those kids, but Kevin particularly had a heart of solid gold and a special place in mine,” he wrote.
He shared photos of Mr Anderson as a boy and from them meeting up again in recent years backstage at his musical The Last Ship.
Sting wrote about Mr Anderson in his autobiography Broken Music, remembering how his pupil had skipped school and put on a high-pitched voice in a phone call to explain his absence.
When Sting – then known as Gordon Sumner – asked who was calling, Mr Anderson replied: “Er… it’s me (my) mam.”
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Sting finished his tribute saying: “I’m completely gutted, I still think of Kev as a cheeky wee bairn, I can’t believe he’s gone.
“God bless ye son, may ye rest in peace.
Mr Anderson’s 28-year-old son Dan got in touch with the musician’s management to tell him about his father’s death.
Pupil and teacher had also previously been reunited for an episode of The One Show.
Sting mentioned in his tribute that when they met some years ago, it was clear Mr Anderson’s life had not been without problems and his son said his father had fought alcoholism and struggled with a skin condition.
Dan said the star looked after his father when he was at school, getting him some trainers so he could go on a trip.
“I think he must have known my dad had it tough, he must have taken a shine to him,” he said.