The 47-year-old was a free agent after leaving Wolves by mutual consent at the end of last season and accepted the role following further talks in London with chairman Daniel Levy and managing director of football Fabio Paratici.
One of his first tasks will be convincing Kane his future lies in north London after the England captain expressed a desire to leave the club this summer.
Kane has dismissed all talk of his club situation as he focuses on England's bid to win Euro 2020, insisting last week he was not even following Spurs' pursuit of Mourinho's successor on social media.
England face Ukraine in Rome at the quarterfinal stage on Saturday and whenever their run at the finals ends, the 26 players will be released to embark on their summer break.
Sources have told ESPN that Nuno is keen to discuss his vision for the team and possible targets with Kane before he departs.
Manchester City have intimated they are prepared to make a £100 million offer for Kane and although a formal bid is yet to be received, Spurs would reject a proposal at that level and are reluctant to see the 27-year-old leave in any case.
Kane has three years remaining on his £200,000-a-week contract and is valued at around £150m. He has scored 166 Premier League goals in 245 appearances and remains a talismanic figure whom Levy wants to retain.
Sources have told ESPN that Paratici played a key role in Spurs opting for Nuno at the end of a search which including conversations with former boss Mauricio Pochettino, ex-Chelsea head coach Antonio Conte and Paulo Fonseca after he left Roma.
Paratici has a strong working relationship with Nuno's agent Jorge Mendes and explored the possibility of appointing him as manager during his 11-year stint as Juventus' managing director.