Spurs have lost five of their past seven league matches, including Saturday’s defeat by Manchester United.
They are eighth in the Premier League and 10 points behind leaders Chelsea.
“I regret that we have had to take this decision,” said managing director of football Fabio Paratici.
“I know how much Nuno and his coaching staff wanted to succeed.”
The Portuguese, 47, was named Spurs manager on a two-year contract in June after four years at Wolves.
“Nuno is a true gentleman and will always be welcome here. We should like to thank him and his coaching staff and wish them well for the future,” added Paratici.
Italian Conte, 52, has been out of work since leaving Inter Milan in May, just weeks after he led the club to a first Serie A title in 11 years.
He won the Premier League and FA Cup at Chelsea but was sacked in July 2018 after a disappointing second year in charge.
The former midfielder has also managed Juventus from 2011-14, winning three Serie A titles, and he took charge of the Italian national team from 2014-16.
Spurs negotiated with Conte following Jose Mourinho’s exit in April but opted not to do a deal amid concern over the Italian’s demands.
It is thought Conte wants to get back into management and he doesn’t appear to be at the top of the list of potential candidates to replace Ole Gunnar Solskjaer, if the Norwegian manager leaves Manchester United.
Spurs, who were booed off following the 3-0 home loss to United, started the season strongly and after winning their first league three matches, Nuno was named Premier League manager of the month for August.
However, the results started to suffer. Despite wins over Aston Villa and Newcastle in October, there were defeats against Chelsea, Arsenal, West Ham and Crystal Palace, as well as a Europa Conference League loss at Dutch side Vitesse Arnhem.
The decision to sack Nuno was taken because of a combination of mixed results, the style of play and fan reaction.
There is sympathy internally as Nuno did not come in at the easiest time and has had to handle a lot of difficult situations, including the summer transfer saga involving captain Harry Kane.
Difficult summer search for new manager
Tottenham conducted a protracted search for a new manager in the summer following the sacking of Mourinho.
They made contact with Paris St-Germain boss Mauricio Pochettino about the possibility of the Argentine returning to manage them but the French club were not prepared to let him go.
Conte appeared set for the role, only for talks between the Italian and Spurs to break down.
Ex-Roma manager Paulo Fonseca then thought he was taking over, only to be sidelined in favour of Gennaro Gattuso, who was rejected when fans reacted badly to the existence of social media posts which brought the Italian’s commitment to inclusivity into question.
No sooner had Nuno been appointed than he had to deal with speculation over Kane’s future, but the Spurs and England captain stayed and an opening-day win over champions Manchester City seemed to have set the tone for a positive season.
However, he has failed to get the most from his star players – most notably striker Kane who has scored just one Premier League goal this season.
The sacking of Nuno Espirito Santo is the conclusion of a shambolic episode that arguably reflects more badly on Tottenham chairman Daniel Levy and his boardroom cohorts than on the departing manager.
Nuno has not lasted much longer than the time it took Spurs to decide to appoint him after a horribly botched and drawn-out managerial search in which potential candidates seemed to appear and disappear in the blink of an eye.
The Portuguese ran out of steam at Wolves after an outstanding reign, leaving at the end of last season, and his counter-punching style of football, well known to anyone who had watched Wolves, was clearly an ill fit set against all the talk of positive football Levy had promised in succession to Jose Mourinho.
Nuno also had to contend with repairing Harry Kane’s relationship with the club as the striker’s form continues to flatline.
A fine start could not disguise the sterile approach and the issues came to a head when Spurs fans rounded angrily on Nuno and Levy during Saturday’s 3-0 home loss to Manchester United. Now the Spurs search begins again.
This can be looked at in two ways. It is either a hasty panic move after only 10 league games or the early recognition of a catastrophic error – either way plenty will feel more sympathy for Nuno than they will for Daniel Levy.