The 25-year-old joined Saints from Huddersfield Giants in 2013 and was contracted until the end of 2017.
Former Castleford back Dawson, who operates mainly at winger or centre, scored 16 times in 70 outings.
"Matty is at a time in his career when he needs to be playing regularly," said Saints chief executive Mike Rush.
"Therefore when the opportunity for him to move to Leigh came up it made sense for the both player and the club to agree to the transfer."
Championship winners Leigh Centurions have signed St Helens utility back Matty Dawson for a five-figure transfer fee on a two-and-a-half-year deal.