The Bulldogs announced Galvin's signing on Friday after the Tigers officially released the want-away five-eighth earlier in the day to end a saga that spanned six weeks of headlines.
"We wish Lachlan all the best with another NRL club," Tigers chief executive Shane Richardson said in a statement.
Galvin has signed a contract with the Bulldogs until the end of 2028 and could be in line to make his Canterbury debut in their King's Birthday clash with Parramatta.
The teen star was excused from Tigers training for Round 13 and omitted from the team to face North Queensland on Saturday as Wests negotiated a six-figure transfer fee with the Bulldogs for his immediate release.
Social media footage appeared to show Galvin on the field at the Bulldogs' Belmore headquarters on Friday, though a club official told AAP he was not taking part in an official training session.
But the NRL is investigating whether Galvin's attendance at their grounds was above-board, given he may not yet have been officially released from his contract at the time.
Galvin's release signals the culmination of a saga that began when he rejected the Tigers' offer of a contract extension last month.
Since then, Galvin has been subject to social media ridicule from teammates Jarome Luai and Sunia Turuva, served the Tigers with a legal letter over bullying claims, and dominated rugby league headlines amid the State of Origin period.
Tigers coach Benji Marshall is eager to move on from the soap opera.
"I guess everyone's probably a little bit sick of talking about it and it being reported," the coach said.
"But we're just focused on the game. I know it's a cliched thing to say, but we have to be.
"It's been a great week at training. Everyone's looking forward to just playing. We had a week off last week with the bye. The energy around the place has been really good, really positive."
Marshall shrugged off questions from the Townsville press as to whether he was disappointed to be losing the young gun around whom the Tigers had planned to continue their rebuild.
"I don't know if disappointment's the word," Marshall said.
"We like the players we've got, we love the squad we've got, we're excited about some of the young players coming through and for us.
"We want to try and make a mark on the competition this year. The squad we've got, we're confident we can do that."
Marshall has named Heath Mason for his first start in the halves at NRL, with the 19-year-old to replace Galvin in the halves next to co-captain Luai.
The Tigers coach has given Mason a simple game plan as the three-time reigning wooden spooners hope to continue good signs on a 5-6 start to the new season.
"We just need our halves to do their job and control the field position," Marshall said.
"We've seen some great glimpses of play from some of our players this year, and we're coming up against a pretty good Cowboys team that have got a lot of great attacking players."
