Son scored twice in five second-half minutes to finish level with Liverpool’s Mohamad Salah on 23 goals as Spurs ran riot to complete an achievement that boss Antonio Conte had described as needing a “miracle”.
Tottenham were ninth when the Italian took over in November and then seven points adrift of fourth when they lost to Burnley in February but 10 wins from their next 14 games saw them overhaul Arsenal, Manchester United and West Ham.
Dejan Kulusevski scored twice and Harry Kane also bagged as Spurs made sure there would be no last-day failure at Carrow Road.
They will return to the premier European club competition after two seasons away and the future looks bright if they can get Conte to commit his future to the club this summer.
Norwich are heading in the opposite direction after another listless display left their home fans chanting against the board and they will have to regroup in the summer ahead of another stint in the Championship.
It never looked like it would be a case of the north London club being ‘Spursy’ as Conte’s side started confidently.
They had an early chance to ease their nerves inside the opening 10 minutes as a quick counter-attack saw Kulusevski cut back to Pierre-Emile Hojbjerg, who blazed over when he should have scored.
That did not matter, though, as they went ahead in the 16th minute.
Hojbjerg’s ball over the top played in Rodrigo Bentancur and as he raced in on goal the midfielder squared for Kulusevski to tap in from close range.
Norwich were almost gifted an equaliser as a sloppy Eric Dier pass allowed Milot Rashica in on goal but he shot wide.
Instead, it was a poor pass at the other end that led to a goal as Spurs doubled their lead just after the half-hour.
Goalkeeper Tim Krul was playing out from the back, but he passed straight to Bentancur, who crossed for Kane to head into an empty net.
Qualifying for the Champions League was the primary goal for Spurs, but the second was for Son to overhaul Salah in the race for the Golden Boot.
He spurned a good chance in the first half as he chose to attempt a first-time volley at the far post when he had time to bring it down.
For large periods of the second half it looked like he would miss out on the silverware as he missed three golden chances.
First he saw an effort palmed away by Krul, who then produced a miraculous save to deny the South Korean from close range after a telepathic cross by Kane.
Then moments later, Kulusevski barged through on goal, rounded Krul and – with an empty net to shoot at – attempted to square to Son, who was tackled by Max Aarons.
The Swede was not going to make the same mistake as two minutes later he out-muscled a defender following Kane’s pass, cut inside and then curled a sublime effort into the far top corner.
Five minutes then changed the course of Son’s afternoon as he scored twice.
After again being denied by Krul, he got another bite of the cherry as Lucas Moura popped off a quick pass and the South Korean found the bottom corner.
Then he put himself in the outright lead as he curled a trademark effort into the far corner from 20 yards to mark mass scenes of celebration.
Salah’s late goal at Anfield did not dampen the mood as Son’s and Spurs’ season ended on a high.