Spurs fended off significant competition from Manchester United for the 21-year-old, who has signed a long-term contract in north London.
The deal eclipses Spurs' previous club record transfer of £65 million to Bournemouth for Dominic Solanke.
"I'm very excited for this next step. Spurs is a massive club and the Head Coach was a key part of why I have decided to join," Fernandes said.
"When we spoke, it was very special. We look at football in the same way - going onto the pitch as a strong team, with fight and energy, to try and win every game. I can't wait to get started, to meet the fans, to meet everyone, and give everything for the Club."
Tottenham have been busy to start the transfer window, with Fernandes the second big-money acquisition after defender Jan Paul van Hecke, who joined for £52 million from Brighton.
They have also brought in defenders Andy Robertson and Marcos Senesi, as well as goalkeeper Martin Dubravka on free transfers.
The arrivals may not end there either, with Spurs closing in on Newcastle midfielder Sandro Tonali.
"I've admired Mateus for a long time because he combines quality on the ball with the intensity and intelligence that are so important in the way we want to play," said Spurs coach Roberto De Zerbi.
"Despite his age, he already has good experience in the Premier League and has shown quality and consistency at this level. Mateus is comfortable under pressure, can progress the ball, works hard for the team and has the courage to make things happen in difficult moments.
"I believe this is the ideal environment for him to continue his development and I'm excited to start working with him."
Fernandes joined West Ham from Southampton last summer for an approximate £40 million fee following the Saints' relegation.
He featured in all 38 of the Hammers' Premier League games, scoring four goals in another campaign that ended with relegation.
Fernandes made his senior Portugal debut in April, but was not selected by Roberto Martinez for the summer's World Cup.