Wimmer, 22, has signed a five-year contract with the London club.
The Austria international moved to Cologne from LASK Linz in 2012 and played 72 times for the Bundesliga outfit.
Tottenham manager Mauricio Pochettino has highlighted defence as one of the??areas where his team needs to improve next season.
Pochettino gave spells to Vlad Chiriches, Younes Kaboul, Federico Fazio and??Eric Dier alongside the near ever-present Jan Vertonghen, but Spurs regularly??looked weak at the back last term.
Despite qualifying for the Europa League, Spurs had the joint-fifth worst??defensive record in the Barclays Premier League last season, conceding 53 goals??in 38 matches.
Wimmer is looking forward to the challenge of breaking into Tottenham’s first??team.
He told Cologne’s website: “Tottenham is a huge chance for me. Nonetheless, it??won’t be easy saying good bye to Cologne.
“I experienced wonderful moments here, such as the promotion and the??Klassenerhalt (staying up).
“I want to thank the training staff, my teammates, and all those involved in??the club for their extraordinary support.
“Cologne and its fantastic fans will always remain something special for??me.”
Cologne general manager Jorg Schmadtke added: “Kevin has improved tremendously??during his time here and has developed into an Austrian international player.
“Of course it is with some regret that he will be leaving us, but we??understand that he is getting the opportunity to play for one of the biggest??traditional clubs in London.”
“In our dealings with Tottenham we were able to reach an agreement that all??parties were happy with.”