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The Blues became champions of England for a sixth time - with two games to spare - thanks to Michy Batshuayi's late goal in a 1-0 win at West Brom.
Conte's side face Arsenal in the FA Cup final on 27 May.
"For me to win in my first season in England, I am really proud of the achievement," he told BBC Sport.
"My players showed me great professionalism, commitment, work-rate and will to try to win this league.
"We have two games to celebrate, then we try to make this season from great to fantastic."
Conte, who took charge at Chelsea after leaving Italy at the end of Euro 2016, says switching to a three-man defence in the wake of a 3-0 defeat by Arsenal in September was pivotal to the Blues' season.
Chelsea were eighth, eight points behind leaders Manchester City after that loss at Emirates Stadium. A 13-match winning streak followed, and they are now 10 points clear of their nearest challengers with two games remaining.
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"It was very frustrating for me because at the end of the Arsenal game I didn't see anything from my work or my ideas on football," said Conte.
"But in this moment I found the strength to change and take responsibility and find a system for the players.
"It was a key moment in the season because every single player found in this system the best for him.
"When you arrive after a bad season and the team has arrived at 10th in the league it means there are a lot of problems.
"To find the right solution quickly isn't easy and for this I want to thank my players because they trusted in the new work, my philosophy, video analysis to see mistakes and they showed the right attitude and behaviour."
Conte apologised after arriving late to his post-match news conference, explaining his players had showered him with beer and champagne and that "my suit is a disaster".
He revealed he had cut his lip as he celebrated Batshuayi's winner, but that it was not the first time he had been injured as a result of his joyful exuberance.
"In these moments, anything can happen," he said.
"I hurt my lip during the Euros as well and they had to put a stitch in it after we scored against Belgium.
"Simone Zaza gave me a header - I don't think it was on purpose. I'm not sure if this was a header or a punch but I am ready to repeat this."
The conference came to an abrupt end when players Diego Costa, John Terry and David Luiz arrived and, impatient to start their celebrations, ushered him away.
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Captain Gary Cahill said the players always believed they could mount a title charge despite finishing 10th last season, 31 points adrift of champions Leicester.
"We felt confident in the dressing room all season," he said.
"We deserved it over the season. We worked very hard and have been the better team.
"It is fantastic to wrap it up with a couple of games to go. It is very difficult in this league."
Fellow defender David Luiz says the chance to land his first Premier League title was one of the reasons he returned to the club from Paris St-Germain in a £34m move in August.
"When I decided to come back here I dreamed to win the Premier League. I am very happy because my dream came true," he said.
"Conte works with passion every day. He deserves it because he is working hard every day."
The Chelsea boss' influence on his side was also acknowledged by West Brom counterpart Tony Pulis.
"They're worthy champions," he said. "They had a poor start, and Conte had to change things.
"He's made it his team. Italian teams are tactically organised and well run.
"He changed their shape and they've been superb from that moment onwards."
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BBC analyst and former Tottenham and Newcastle midfielder Jermaine Jenas believes Conte deserves the credit for turning the club around, highlighting his conversion of Victor Moses from a fringe midfielder to first-choice wing-back.
"They lost their way last season, they were unrecognisable. He has come in and reinvigorated them," Jenas said.
"What I like about Conte is he gave Moses a chance and trusted him. He has made him a better player and a Premier League champion."
Chelsea need to win the FA Cup to turn a "great season" into a "fantastic" one after clinching the Premier League title, says manager Antonio Conte.