The 24-year-old prop has been loaned back to the Rams with immediate effect, but will train with the Saints squad.
Saints CEO Mike Rush said: “We’re delighted to have agreed terms with Matthew. He is a forward of promise and we look forward to seeing him develop within our system.
“We are constantly looking for new talent throughout the Rugby League pyramid and Derek Traynor, Head Coach of our 19s, recommended we took a look at Matthew.
“We like what we see and we are pleased to have reached an agreement with the Rams. They have been very professional in our dealings.
“Matthew will train for us during the week and play with Dewsbury where we will monitor his progress.”
Haggerty will join up with Saints on March 1. He played his junior rugby at Leigh Miners Rangers before joining Salford in 2008.
Since then, he has played for Whitehaven, Barrow and Oldham, before joining Dewsbury. He is relishing the challenge ahead of him at Langtree Park.
“I am excited by the opportunity of taking a contract with Saints but at the same time sad to be leaving Dewsbury although I will be staying with them for the rest of the season,” he said.
“I’d like to thank Mark Sawyer for giving me the chance and Glenn Morrison for the hard work he has put into me over the last two seasons to get me in a position were a club from Super League shows interest.
“When they signed me my career was in the balance and to be honest I’d lost my confidence. Glenn and the great atmosphere in the changing rooms got me back on track. I’d like to thank all the lads and the fans very much.
“I’m really excited to be joining such a great club in Saints and with the current crop of players I’m sure we will be challenging for honours for years to come.
Dewsbury Chairman Mark Sawyer confirmed that there had been interest from other Super League clubs in the player too.
“In recent weeks three Super League clubs have shown an interest in Matthew,” he said.
“I would like to thank St Helens for the professional manner in which they have dealt with the transfer, but also in the compensation package they offered to the Rams.
“This includes Matthew being loaned – at Saints’ cost – back to us for the rest of the season along with a friendly game at Langtree Park. These, along with the other elements, made it a very acceptable agreement.
“It is important young players have the chance to step up to Super League should the chance arise. I will be sad to see Matthew go but I for one will watch his progress with great interest.”
Rams coach Glenn Morrisonbelieves that Haggerty has improved massively as a player over the last year.
“We identified Matty while he was with Barrow and continued to keep tabs on his progress when he was playing in Championship 1,” he said.
“He’s a good kid who has always been eager to learn and he’s really developed as a player during the last 12 months.
“We always knew there was something there and that’s been proven by this approach by St Helens. It’s a great opportunity for him.
“It’s great for him that a club like Saints has come on for him and a good reflection on the club that we’re developing players of this calibre.”