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.
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.
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.