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."

It's letting you search for every public tweet since its creation in 2006, roughly half a trillion posts.
On the one hand, it could be seen as a helpful and extensive tool for information.
On the other, it could flag up any user who may have forgotten about a potentially embarrassing post from their distant past.
In theory, it means anyone can look back at your FULL tweet history.
If you so wished, you could go back to the beginning of your timeline and see just how mundane - or thrilling - your early tweets were.
Perhaps more interestingly, you can search through your friends entire history, as long as they were posting publicly.
In a blog post which explains the complexities of its update, Twitter's said the new search service has been several years in the making.
Before, the search would give you a limited amount of results, with a focus on an individual's recent history or the recent appearance of a hashtag.
The advanced search has been expanded, offering you the chance to look back through a specific time period, with specific words or for a specific user.
If, for example, you search for a hashtag it will eventually start giving you the results it thinks are most relevant from its entire history in the 'top' tab, instead of the 'all' tab next to it.
You can now search for the earliest times a certain phrase or word was mentioned on Twitter.
The same goes for tracking a certain hashtag.
For example, did you know that Chris Messina, a former Google executive, was the first person to start using hashtags on Twitter back in 2007?
He's also the first person to have ever posted #justsayin.
The first time the word 'totes' was used on Twitter was in 2006, four years before it came to prominence in TOWIE.
Because of the size of the database, it takes an effort to go through every mention of One Direction, Katy Perry or Rihanna.
It's handy though for uber fans wanting to know exactly when and where their idols were in their early days.
For some, the prospect of a boss or parents looking back through your entire history with relative ease may fill some people with dread.
However, the tools were already in place to delete past tweets through Twitter itself and third party sites.
Twitter allows you to request your full Twitter history in which you can search for anything you don't want to be seen publicly anymore.
The new search will be rolled out to all users in the coming days.
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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.
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Twitter's rolling out a feature which could instil fear into your social media hearts.