The 24-year-old has agreed to join the north London outfit until 2021 after successfully completing a medical, and becomes their first signing of the summer
Wanyama is the first Southampton player to be reunited with the club's former manager Mauricio Pochettino at White Hart Lane.
Press Association Sport understands Tottenham will pay around £9million up front for Wanyama, but the deal could reach almost £12m if additional clauses are met.
Spurs first expressed an interest in Wanyama last summer but Saints held firm and were rewarded, as Wanyama played a key role in leading the team to a sixth-placed finish
The Kenyan, who had just one year to run on his contract at St Mary's, made 85 league appearances for the south-coast club, scoring four goals
Pochettino has been eager to boost his options in midfield with Tottenham hoping to balance Champions League football with another title challenge next season
The Argentinian is also eager to bring an extra forward to provide cover for Harry Kane but Spurs are yet to follow up talks with AZ Alkmaar striker Vincent Janssen.
Janssen visited Tottenham's training ground two weeks ago and spoke to the club about his future but Tottenham have not submitted an official bid
The Dutch striker is currently on holiday in Barcelona and has also held talks with German club Wolfsburg, although a move to Spurs remains the 22-year-old's preferred choice
Source : PA
Source: PA