Michy Batshuayi's goal eight minutes from time earned Conte's side a 1-0 win at West Brom and ensured they clinched the trophy at the earliest opportunity. The double could follow if Chelsea can beat Arsenal in the FA Cup final on May 27.
And Conte can expect to be rewarded for a successful season with a new contract offer 12 months into the three-year deal he signed on joining last summer.
The former Juventus and Italy boss has so far been equivocal over his future with Inter Milan making overtures. But the 47-year-old suggested after the title success at The Hawthorns that he wanted to build on the rejuvenation he has led this season.
He said: "We started to do our work. We have to improve in the next season, to find the right solution to improve. We are working (for) only nine months together. I think if you can continue with these players you can improve a lot.
"Now they know my idea, I know them, the characteristics of my players. And we can improve."
Conte wants to keep his best players and strengthen his squad ahead of next season's Champions League return, but there is fervent speculation over the future of striker Diego Costa, in particular.
The Italian said: "The club want to fight to win every competition. We have the same ambition. For this reason we try to keep the best players."
Conte kept his composure during a huddle with journalists as Costa lurked menacingly, threatening to put a dampener on celebrations by jokingly brandishing a fire extinguisher.
The Italian had already been drenched by champagne, iced water and beer in the dressing room, forcing a change of clothes, before his post-match media conference was brought to an abrupt halt by Costa and David Luiz.
The pair then impatiently waited, with club captain John Terry standing guard to make sure nothing untoward happened, as Conte fulfilled the further media commitment.
Luiz monitored the time taken for questions and Costa held the fire extinguisher aloft in the direction of journalists.
The pair were attempting to speed up proceedings to resume celebrations with the head coach who had steered Chelsea to a second title in three years after last season's 10th-placed finish.
Conte has won the last four domestic championships in which he has managed, having claimed three in a row with Juventus prior to being Italy boss.
The Italian had seen the potential in a team which won the 2014-15 title under Jose Mourinho before imploding within months.
At his unveiling on July 14 last year, Conte said: "I hope there is a small flame flickering that can eventually grow into a blazing inferno."
Costa had threatened to douse the flames and jeopardise the title bid in January, when he apparently had his head turned by a lucrative offer to join Chinese Premier League side Tianjin Quanjian.
Conte refused to discuss reports of a disagreement with 20-goal Costa in public, attributing the striker's absence from the Premier League trip to Leicester to a back injury.
"I think in every season there are moments you have to find always the right solution," Conte added. "For this reason I have to say thanks to my players. They showed me in every moment great attitude, great work rate and to trust in my work. It's right now to celebrate."
Conte's focus has already moved on to the next target. Chelsea conclude the Premier League season with home matches against mid-table Watford and relegated Sunderland before the FA Cup final.
When it was put to him that Chelsea could have two weeks off to prepare for the Wembley date with Arsenal, Luiz interjected.
The Brazil defender said: "Rest? Rest for you. We train every day."
Conte, laughing, added: "They know we have to work during the training session to prepare in the right way these two games against Watford and then Sunderland.
"When you work hard it's important to celebrate and then to prepare in the right way the final of the FA Cup, because we have the opportunity to fight to win the double and we must be ready to do this."
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