The experienced hooker has been at the AJ Bell Stadium since 2014, captaining the team in 2016, having previously spent time at Wakefield, Huddersfield and boyhood club Hull FC, amongst others.
Lee has now agreed a two-year deal to move to Langtree Park as Saints continue to build towards the 2017 campaign.
Coach Kieron Cunningham believes the 28-year-old's versatility can prove to be a major asset while he has also praised the other attributes he can bring to the dressing room.
"Tommy is a versatile player who can play at nine, in the halves and at loose forward, taking pressure off James Roby," said Cunningham.
"He is experienced and his leadership and composure will be vital in our young squad as we look to challenge for honours this season."
The Merseyside outfit have already added props Adam Walker and Luke Douglas plus winger Ryan Morgan and half-back Matty Smith from local rivals Wigan.