The 22-year-old has penned a five-year deal and will officially arrive at White Hart Lane when the transfer window re-opens for business on 1 July.
But just who is he? IBTimes UK has the lowdown on the Premier League's newest recruit;
A centre-back by trade, Wimmer joined Cologne from Erste Liga side LASK Linz three years ago and made 22 appearances for the club in 2013/14 as they won promotion to the top tier of German football for the first time in two years after winning the 2. Bundesliga with a six-point margin over SC Paderborn 07.
His impressive development under Peter Stoger continued last term as he featured in 34 games in all competitions, helping his team to finish 12th and comfortably clear of the relegation dogfight.
According to WhoScored.com, each of Wimmer's 32 league appearances last season came in the heart of defence.
He won 92 out of 158 aerial duels in that time, made 42 interceptions, contributed 206 clearances and blocked 31 shots. He received four yellow cards and one red but did not manage to register a single goal or assist.
As well as impressing for his club, Wimmer - previously a regular at U21 level - is also a full Austrian international after being awarded his first cap by Marcel Koller during the closing stages of the 1-0 friendly victory over the United States at Ernst-Happel Stadion in November 2013.
Having been left on the bench for the narrow defeat to Brazil, his second overall appearance and first senior start for his country came in March when he featured for the full 90 minutes of a 1-1 draw with Bosnia and Herzegovina.
Koller, who could persevere with Wimmer for the upcoming Euro 2016 qualifier against Russia, has previously spoken of the player in glowing terms and expects him to improve further with consistent exposure to the highly-competitive world of Premier League football.
"He [Wimmer] has played exactly the same as I've seen him from him already with Cologne," he said back in April.
"On the ball he is very quiet, not rushed. He moves in the summer to England. With his younger years, he still has the potential to improve. He has it all."
Tottenham fans will certainly hope he can hit the ground running in north London after Mauricio Pochettino's side conceded 53 goals - more than any other team in the top 10 - during the Argentine's first year in charge and finished with the joint-fifth worst defensive record in the top-flight.
Vlad Chiriches and Younes Kaboul are both expected to depart over the coming months, while Wimmer's key rivals for a starting berth will likely be Jan Vertonghen, Eric Dier and Federico Fazio.
Further defensive strengthening can also not be ruled out as chairman Daniel Levy continues to pursue a policy of securing talented young players for relatively modest fees after largely squandering the windfall earned from the sale of Gareth Bale to Real Madrid on signings who have flattered to deceive.