Second-row player Tupouniua, who turns 22 later this month, penned a two-year extension, as did centre Smith, who is currently rehabbing a knee injury.
23-year-old prop Faamausili agreed to a three-year extension.
Tupouniua and Faamausili made their NRL debuts last year and have each made several appearances off the bench in 2019 for the 8-2 Roosters.
Smith, the youngest of the trio, is yet to make his NRL debut.
Sydney coach Trent Robinson expressed his delight at the signings.
“It’s been great to watch the development of Sitili, Poasa and Billy over the years,” Robinson told the club’s website.
“In their own right, their work ethic precedes them, and they embody the values we want in our players both on and off the field, so it’s really pleasing that they will continue to represent our club and our area.”
The Roosters will look to bounce back from last week’s shock loss to the Broncos when they travel to Newcastle to take on the Knights on Friday night.