Son has signed a five-year deal with the north London side for a reported transfer fee of £22 million ($34 million, 30 million euros), with the 23-year-old's move to White Hart Lane subject to a work permit and international clearance.
Son scored 29 goals in 87 appearances for Leverkusen after joining from domestic rivals Hamburg in 2013 for 10 million euros.
Leverkusen have already signed his replacement in Slovenia international Kevin Kampl from Borussia Dortmund.
Born in Chuncheon, the capital of Gangwon Province, Son - nicknamed 'Sonny' -- joined Hamburg's youth set-up at the age of 16 and first played for South Korea in 2010.
His move will give Tottenham an extra forward option, with rising star Harry Kane yet to score this season.
Should Son's transfer be confirmed, it may mean that Spurs' pursuit of Saido Berahino is at an end, with the club having already had two offers for the West Bromwich Albion striker rejected by their Premier League rivals.
Son has 11 goals in 44 international appearances and played at the 2014 World Cup.
“I'm looking forward to going there and performing for the Spurs fans as soon as possible,” Son told Tottenham's Twitter feed. “The support I get from the fans motivates me more and more.
“I'm a player who really loves football. I learned the game under my father who was a football coach in my school.
“I've trained with both feet so I can use them freely. Bold and daring -- this is how I like to try to play.”
Son leaves Leverkusen on the back of a public spat, though, after missing Wednesday's Champions League play-off victory over Lazio in order to complete his Spurs move.
Both Bayer Leverkusen coach Roger Schmidt and Son's team-mate Haken Calhanoglu had criticised Son for the timing, saying the Korean had been “ill-advised”.
But the striker took exception to Calhanoglu's comments after the Turkish midfielder forced through his transfer from Hamburg to Leverkusen last year.
“People who lives in glasshouses shouldn't go throwing stones,” Son told German Kicker magazine.
“Everyone should mind his own business and there is certainly enough to take care of.” – AFP
Original source: Spurs sign S Korean forward