The 30-year-old winger was signed from Aston Villa by former Hoops boss Brendan Rodgers in 2016 and scored the winner against the Jambos at Tynecastle on his Ladbrokes Premiership debut.
The Parkhead club, who recently secured their eighth successive title win, have the chance to clinch an unprecedented triple treble against the Tynecastle club at the national stadium.
Sinclair said he was “delighted” that a one-year contract clause was triggered at the start of this month and added: “Hopefully we can make it a treble. Not just for myself but for the whole team.
“It has been a great time and we have to make sure we get the job done.
“Being part of the double treble as a player has been great. It is a massive achievement.
“When I came up here you are not even thinking about double trebles or treble trebles, you come and work hard and see how it goes.
“I couldn’t have asked for anything better. It comes down to hard work and the winning mentality of the players.”
On staying at the Parkhead club for another season, the former Manchester City and Swansea player said: “I always wanted to stay. Everyone knows my situation and how I love this club and I want to be here.
“I love the fans and playing for Celtic. I am here for another year and I am looking forward to it.”