The Blues advanced to the showpiece with a 2-0 victory over Southampton on Sunday, thanks to a goal each from Olivier Giroud and Alvaro Morata in either half at Wembley.
That win sets up another date at the 'Home of Football' with Mourinho's men, who downed Tottenham the previous day to reach the final.
Conte and Mourinho have clashed publicly on numerous occasions, but the Chelsea boss insists that any issues the pair might have had are firmly in the past.
“With Jose, we have clarified the situation. This is the most important thing," Conte explained to reporters after the final whistle.
"There is not a problem between him and I. I think this final is a game between two great teams: Manchester United and Chelsea.
"For sure, in my mind, I can tell you that we played last season in the final and arrived as favourites against Arsenal. This season, we are arriving not as favourites. But, as you know very well, we lost the final despite being favourites in my mind.
“We are talking about two managers with strong characters, and two winners. When in your mind and your heart and your blood there is the will to win, for sure, we want to try to win this trophy.
"The same way Manchester United want to do this. I repeat. I have great respect for United's story, for Mourinho's story. They have the same respect, I think, for Chelsea's story and my story.”
Giroud boosted his excellent record at Wembley with a match-winning performance, and Conte was delighted to see his January signing take centre-stage.
"He has been a good signing for us. As you know very well, I needed a player with this characteristic: strong physically, to hold the ball up and allow our No. 10 to make combinations with him," he added.
"Morata is an important striker. I think he's younger than Olivier. He has less experience. He is less strong physically but, at the same time, is very fast to act on the space.
"I'm pleased for both, for both, because in the last game against Burnley we started the game with both players and they showed a great link-up. I'm very pleased to see that, because I have another option now. Another card in my hand during the game.
"Today I decided to start with Olivier because I knew we had to play against the three central defenders, very strong physically, so I decided to start with Olivier. But when Morata came on, the impact was impressive. In the same way as Pedro's impact, which was important. And also [Tiemoue] Bakayoko.”