The Saints received Richmond's pick No.14 and Carlton defender Natalie Plane in exchange for Greiser, while Tigers defender Harriet Cordner has joined the Blues.
Greiser, 24, who has booted 29 goals in 34 games, will deliver the Tigers much-needed firepower alongside skipper Katie Brennan following Courtney Wakefield's retirement.
She was an All-Australian, league leading goalkicker and St Kilda best and fairest winner in her debut season in 2020, when she burst onto the scene with 10 goals.
"We are delighted to bring Caitlin to our club and expect her skill set to be able to help us right away," Richmond women's football boss Kate Sheahan said.
"Caitlin is a proven performer at AFLW level and an excellent person with a character that will fit right into what we are trying to build here."
The Saints have been linked to a move for Brisbane spearhead Jesse Wardlaw and pick No.14 could be helpful in sealing a trade for last season's leading goalkicker.
The recruitment of former Magpies Steph Chiocci and Jaimee Lambert has given St Kilda extra midfield class but Plane, 26, provides defensive reinforcement.
"Natalie's experience will be a great asset to our playing group, with the way she drives elite standards and pushes her teammates to do the same," Saints AFLW boss Tessie McManus said.
Experienced key back Cordner, 30, spent four years at Melbourne then three at Richmond and will front up for the Blues after missing all of last season with a knee injury.
"With 37 games to her name, Harriet will already be in the top five most experienced players on our list, so her knowledge of what it takes to consistently compete at the elite level will be crucial for our group," Carlton football boss Brad Lloyd said.
"Harriet is a proven leader, who we know will help us drive standards internally and be a strong voice to help guide the emerging talent we have throughout the playing list."
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