Spurs face the unenviable task of taking on holders Real Madrid and Borussia Dortmund in Group H, as well as Cyprus’ APOEL.
“It’s a great draw,” Kane said.
“You expect to play the best in Europe in the Champions League and it’s exciting for us. We look forward to these games.
“You want to test yourself against the best and Real Madrid are the best at the moment.”
The draw sees Gareth Bale and Luka Modric face their former club after in June helping Real become the first team in the Champions League era to win back-to-back titles.
Scottish champions Celtic are also in a challenging pool, against Bayern Munich, Paris St Germain, and Anderlecht in Group B.
Manchester City, Liverpool, and Manchester United, in particular, will be confident of progressing to the knockout stages following yesterday’s draw in Monaco.
Chelsea, in 2012, were the most recent champions from Britain.
The final takes place at the NSK Olimpiyskyi in Kiev on May 26, 2018.
Among the intriguing sub-plots is the draw which saw Premier League champions Chelsea, on their return to Europe’s elite competition after a single-season absence, pitted against Atletico, Roma, and Qarabag — the first Azerbaijan side to reach the group stages — in Group C.
Costa was playing for Atletico when Chelsea last faced them in the Champions League, in the semi-final in April 2014, and joined the Blues three months later.
He scored a penalty as Atletico won 3-1 at Stamford Bridge, progressing by the same score on aggregate.
Goalkeeper Thibaut Courtois was on loan at Atletico then and helped the Spanish side to the final at his parent club’s expense.
Former Blues Fernando Torres and Filipe Luis are now at Atletico, whom Costa wishes to rejoin.
Costa has been an unauthorised absentee from London in recent weeks as he agitates for a move back to his former club. The Brazil-born Spain striker and Chelsea are in dispute about the version of events.
Chelsea say it was decided in January with Costa and his agent, Jorge Mendes, that the striker could leave in the summer.
Costa, though, claims he is being forced out by head coach Antonio Conte.
The situation is complicated by a transfer embargo which prevents Atletico from registering new players until January.
Antonio Rudiger will face his former club Roma, while the Blues must travel to Baku in November to face Qarabag.
Manchester United, who qualified by winning the Europa League in May, received a favourable draw in Group A alongside Benfica, Basle and CSKA Moscow. United boss Jose Mourinho is seeking a win with a third club after victory in 2004 with Porto and 2010 with Inter Milan.
Manchester City will face Shakhtar Donetsk, Napoli, and Feyenoord in Group F.
City director of football Txiki Begiristain said: “It’s going to be a good group of good football.
“Our target as a football club is to be consistent in our performances in Europe.
“It means we are always in quarter-finals, semi-finals and why not play in a final? This is our target.”
Begiristain was dismissive about the prospect of Argentina playmaker Lionel Messi moving to City from Barcelona.
He said: “I heard a rumour he had signed a new contract. He’s going to stay there.”
Five-time winners Liverpool will play Spartak Moscow, Sevilla, and Maribor in Group E.
Liverpool boss Jurgen Klopp says his side can do well if they repeat their performance in the play-off second leg win over Hoffenheim.
“The first 20 minutes were probably part of the best pieces of football I was ever part of,” the German said.
“But we have to replicate this. Then we can be successful.
“That’s good news but hard work also.”
It is only the second season that five clubs from one nation were in the group stage, after Spain had five representatives in 2015-16.
Teams from the same association cannot face each other in the group stage and just two groups featured non-British teams.
Juventus, runners-up in Cardiff in June, face Barcelona, Olympiacos, and Sporting Lisbon in Group D.
Group G features Monaco, Porto, Besiktas, and Red Bull Leipzig.