Mourinho was relieved of his duties after 17 months in charge of the North London outfit, having replaced Mauricio Pochettino at the helm in November 2019.
The former Chelsea and Manchester United manager has guided Tottenham to the Carabao Cup final, where they will meet Manchester City at Wembley this weekend but he will not be able to take charge of proceeding from the dugouts.
Mourinho helped Kane and Son form a formidable partnership in the Tottenham Hotspur attack, which has seen them score 34 Premier League goals between them this season.
Posting on Twitter, Kane wrote: "Thank you for everything Boss. A pleasure to have worked together. I wish you all the best for your next chapter."
Son added on an Instagram post: "I have no words to describe how I'm feeling, it's been a pleasure to work with you, I'm sorry things didn't work out and truly grateful for the time we've had together.
"Good luck and all the best for the future."
Tottenham are seventh on the Premier League table, five points behind West Ham United in fourth.
Mourinho took charge of 86 games as Tottenham manager, winning 44, losing 23 and drawing 19.
