The former Olympique de Marseille defender enjoyed a good rapport with the Portuguese tactician at Stamford Bridge from 2013 to 2015, winning the Premier League and the League Cup.
Mourinho went on to manage Manchester United after he was sacked by Chelsea in December 2015 following a poor start to the 2015-16 season.
The Spanish international has insisted that though Mourinho has gone to a London rival, he wishes him nothing but success.
"I can talk only when Jose was here at Chelsea with us," the 30-year-old told Sky Sports News.
"We won trophies, and now football moves on. I wish him all the best even though he goes to a rival. I have good memories with him and I have played many times under him and against him.
Former Chelsea goalkeeper Petr Cech also joined Azpilicueta to wish ‘one of the most successful managers’ the best of luck and has admitted that Mourinho coming back is great for the Premier League.
"He's a great manager and obviously it's great for the Premier League to welcome back one of the most successful managers of the past 15 years, so obviously we wish him well," Cech said.
The former Real Madrid and Inter Milan manager’s first test as a Tottenham Hotspur manager comes on Saturday when his side make a short trip to West Ham United.