Leverkusen, who will face holders Barcelona, AS Roma and BATE Borisov in their Champions League Group E, said the 24-year-old attacking midfielder signed a five-year deal.
Kampl had played as a teenager for Leverkusen before stints at several lower tier German clubs, Salzburg, where he played under current Leverkusen coach Roger Schmidt, and then joined Borussia Dortmund at the start of this year.
South Korean forward Son had earlier in the day signed with the Premier League club forcing Leverkusen to act fast with the transfer window closing in a few days.
The German club had also seen Chile international Charles Aranguiz sustain a torn Achilles days after joining this month, an injury which will rule him out for several months.
"Kevin Kampl can be deployed in several positions, he is fast and has the special quality of putting his teammates into play," said Leverkusen sports director Rudi Voeller in a statement.
"We now have several possibilities with Kevin joining and are happy he decided to come here."
Kampl had failed to carve out a starting spot under former Dortmund coach Juergen Klopp last season and had played only a minor role under his successor Thomas Tuchel so far this season.
Tottenham, with only last season's top scorer Harry Kane as a proven striker, have been keen to sign another attacking player and will give Son their number seven shirt, the club said on Friday.
Their website (www.tottenhamhotspur.com) described him as "a consistent goalscorer throughout his time in Germany" one with 11 international goals in his 44 appearances for South Korea to date, including scoring against Algeria at the 2014 World Cup finals.
"Spurs is such a big club and a really good team," Son said in an interview translated from Korean.
"My goal has always been to play in the Premier League and I have a great opportunity to do that now with Tottenham – I am really happy about this.
"I am also very pleased and honoured to work together with good players such as Harry Kane, Christian Eriksen and all the players at Spurs.
"I’ve tried hard to learn many things throughout my career so far, I’ve played many games already and gathered a lot of experience for my age.
"That makes me play better and score goals. Bold and daring – this is how I like to try to play."
Spurs were left short of attacking threat after Roberto Soldado left for Villareal, while Emmanuel Adebayor no longer figures in manager Mauricio Pochettino's plans.
They have tried in vain to sign Saido Berahino from West Bromwich Albion.
(Reporting by Karolos Grohmann and Steve Tongue; editing by Amlan Chakraborty)
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