Ryan Mason filled in as caretaker boss following Mourinho's sacking in April, steering the club through to the end of the 2020-2021 season.
Former Spurs boss Mauricio Pochettino was linked with a sensational return, while Antonio Conte, Paulo Fonseca and Gennaro Gattuso were all rumoured to be on the verge of filling the vacancy at different stages in the process.
However, the London club has instead turned to Nuno after his four-year spell with Wolves came to an end in May.
The 47-year-old Portuguese has signed a deal until 2023 with Tottenham, where he will work alongside new director of football Fabio Paratici.
"When you have a squad with quality and talent, we want to make the fans proud and enjoy," Nuno said following his appointment.
"It's an enormous pleasure and honour (to be here), there's joy and I'm happy and looking forward to starting work. We don't have any days to lose and we must start working immediately as pre-season starts in a few days."
Nuno earned promotion to the top flight in his first season in charge at Wolves, then followed that achievement with successive seventh-place finishes in the top tier.
He also reached the quarter-finals of the Europa League in the 2019-2020 season but, following an underwhelming 2020-2021 campaign – not helped by a long-term injury sustained by Raul Jimenez in November, plus the sales of Matt Doherty and Diogo Jota – he left by mutual consent.
Nuno starts his new role amid uncertainty over the future of England captain Harry Kane, with Manchester City reportedly bidding £100million for the prolific striker.
"First of all, I'd like to welcome Nuno to the club," Spurs chairman Daniel Levy said. "We should like to thank our supporters for all their patience throughout this process.
"I've spoken already about the need to revert back to our core DNA of playing attacking, entertaining football and Fabio and I believe Nuno is the man who can take our talented group of players, embrace our young players coming through and build something special."