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 smashes Spurs' previous record transfer of £65 million to Bournemouth for Dominic Solanke in August 2024.
The record may not stand for long, though, with Spurs having also agreed a £92.5 million move for Newcastle midfielder Sandro Tonali, plus £7.5 million in add-ons.
"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."
Fernandes is Tottenham's second big-money acquisition this summer 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.
Fernandes joined West Ham from Southampton last summer for an approximate £40 million fee following the Saints' relegation.
He featured in 36 Premier League games for the Hammers last season, scoring three goals in another campaign that ended with relegation.
Fernandes made his senior Portugal debut in March, but was not selected by Roberto Martinez for the summer's World Cup.