The Centurions, who will play in the Qualifiers after finishing in the bottom four, have made their move ahead of Friday's transfer deadline, securing the services of the 22-year-old front-rower on a contract to the end of 2018 with an option for a further year.
Richards was a member of Saints' 2014 Grand Final-winning team but has made only three appearances this season and has been playing on a dual registration for Sheffield Eagles.
Leigh coach Neil Jukes said: "Greg has been at an elite club for a number of years and played a lot of games. He is going to bring good habits and plenty of experience, even though he has youth on his side.
"Greg has really bought into our vision and what we want to achieve at Leigh Centurions. He sees the opportunities that are in front of us but first of all wants to be part of achieving our goals of maintaining our Super League status.
"Greg will add competition and energy to the middles and he has shown he can do it at the highest level."
Richards will help plug the gap created by the early retirement of Leigh's Australian forward Dayne Weston.
St Helens chief executive Mike Rush said: "It's always tough when a player who has been through the system at the club leaves for pastures new.
"There has been strong competition for places here this season though and therefore, reluctantly, it made sense to allow him to join Leigh.
"We wish him the very best in his future career."