The 29-year-old makes the move after two seasons with the Saints.
He played in 39 games since signing from London Broncos, scoring 10 tries.
Saints Chief Executive Mike Rush said: “We’d like to wish Tils all the best at Leigh Centurions.
“He has proved a popular member of the squad here and we’d like to thank him for his efforts in the red vee.
“Like any former player, he will always be welcome back at the club.”
Atelea made his first-grade debut for Cronulla in 2009, before moving to Melbourne Storm in 2011 and St George-Illawarra a year later.
The 6ft, 16 stone forward was then picked up by the Broncos in 2014 and led the way in making more than 1,700 metres and busting nearly 60 tackles.