Spurs named Mourinho their new manager less than 12 hours after dismissing Mauricio Pochettino, the man who led them to the UEFA Champions League final last season.
Results have soured this term and Pochettino left the role on Wednesday (AEDT) without having added to the club's trophy cabinet.
Tottenham great Gascoigne thinks Mourinho is the man to buck the trend of near-misses and, despite his adversarial managerial style, expects a reportedly fractured set of players to unite behind the new boss.
"The way Manchester City have put pressure on everybody, people are looking for the best," Gascoigne, who won the FA Cup with Spurs in 1991, said.
"As far as I'm concerned, Jose Mourinho is an unbelievable manager.
"If I was a Tottenham player now and knowing Jose Mourinho was going to be manager I would be more than happy.
"Have you had a look at what Jose Mourinho has won? Jesus. Alex Ferguson was an unbelievable manager, the best ever in the world, and Jose Mourinho isn't far from him."
Asked whether it might take time for Mourinho to win over the dressing room, Gascoigne replied: "I wouldn't have thought so. Definitely not, no way.
"There will be sadness because obviously a lot of players were close to Pochettino and I feel sorry for him. I suppose he will go on holiday and have a think about what he wants to do next. I'm sure a great club will come in for him.
"The players will warm to [Mourinho] and if they don't they'll be on the bench. He's definitely a manager I would play for, that's for sure. A manager is only as good as the players he's got and if he's not happy with the players he's got he will bring in players."
The Tottenham Hotspur Supporters' Trust said it was "shocked and saddened" by the decision to dismiss Pochettino, who spent more than five years in charge, but Gascoigne reckons fans can look forward with optimism.
"All they have to look at is Jose Mourinho's trophy cabinet," he said.
"The players have got to understand they haven't won anything. Jose Mourinho has – what he has achieved as a manager is second to none.
"Tottenham's future looks bright and if I was a Tottenham supporter now I'd be more than excited."