The Dragons confirmed the news on Tuesday, with the 23-year-old set to depart the Rabbitohs after only three seasons at Redfern.
Su'A began his career with the Broncos in 2016, making his NRL debut with the side at 18 years of age.
After spending the best part of four seasons in Brisbane, Su'A followed ex-Broncos coach Wayne Bennett down to Sydney and signed with the Rabbitohs mid-year in 2019.
Season 2020 was his breakout year with the backrower making 592 tackles, 21 offloads and averaging 101 running metres per game as the Souths finished sixth and Su'A made his State of Origin debut for the Queensland Maroons.
Speaking to the club's website, Dragons General manager of football Ben Haran exclaimed his delight at securing Su'A's signature.
"We have made no secret that strengthening our pack has been a recruitment priority for us of late and we're pleased to bring a player to the club of Jaydn's quality," Haran said to Dragons.com.au.
"While only young, he is at good stage of his career having already played representative football at a State of Origin and international level.
"The most exciting thing about the recruitment of Jaydn over the coming three seasons is the extra dimension he will add to our squad."
St. George Illawarra find themselves just inside the eight in 7th position and will hoping for a strong finish to the season to secure a finals berth.
Their next encounter comes against the Titans on the Gold Coast on Sunday, with Anthony Griffin hoping his side can secure a victory on the road despite the suspensions they are currently working their way through after the biosecurity breach from a fortnight ago.