Conte was appointed at Tottenham earlier this month and promoted Mason to first-team coach.
Mason said: "It's pretty strange to be honest. When I had my injury, it was against his team at Stamford Bridge.
"He came to the hospital afterwards to see me and my family. I don't really recall that to be honest because of the nature of my injury, but there's a photo where he's with me at my bedside and I think that shows what type of man he is – a very, very classy individual.
"Then my only England cap was against his Italian team out in Italy in 2015, so there's that history there and hopefully we can come together and create some positive history for Tottenham now."
He added: "I'm delighted and very excited to join the team under the boss and also the staff that he's brought along. It's an exciting chapter for the football club, we'll be looking to work hard, improve and get some positive results in the short term, but also in the long term as well."