The left-sided full-back has joined from Liverpool, signing a deal until 2024.
It comes a day after Ali Crawford made his loan move from Bolton Wanderers permanent, while Reece Devine and Lars Dendoncker had their loans cancelled.
Davidson is looking to reshape his squad with the team bottom of the table after a disastrous first half of the season.
Gallacher moves north having been at Liverpool since he moved to the club from Falkirk for a six-figure fee in 2018.
He made one first-team appearance for the Anfield club and enjoyed a short-loan spell with Toronto FC in MLS.
"I'm really excited about my move to St Johnstone and can't wait to get started," Gallacher told the club's website.
"I had a great time at Liverpool and I'd like to thank everyone there for looking after me and helping me to improve as a footballer and teach me so many good habits.
"I feel very lucky to have been part of a massive Football Club with so many wonderful professionals and people. It was an incredible education.
"But I felt the time was right to look for first-team football and an exciting opportunity presented itself at St Johnstone.
"Having been out on loan at Toronto, I enjoyed my time there and it made me want more and more first-team football.
"It's now up to me to show everyone at St Johnstone that I'm good enough to play regular first-team football and that's what I plan to do.
"My preference is to play on the left-hand side as I feel I have good energy to get up and down and can deliver crosses into the box. I also enjoy the defensive side of the game.
"My immediate aim is to work hard and integrate with the group. Team spirit is so important and I know it's a really good squad at St Johnstone.
"There will be a feeling of positivity going into the second half of the season. We then need to take that into games and we will.
"It's vital to win games of football and I am confident we will do that to move away from the bottom end of the table."