The 24-year-old former Geelong and Carlton defender met with the Swans on Thursday and the club lodged the paperwork on Friday.
Laidler appeared to fall out of favour with new Blues coach Mick Malthouse and played just one game in 2013.
He had established himself as a key part of the Blues' defence in 2011 but a knee injury in 2012 derailed his form and restricted him to just three games.
The Swans had a tumultuous trade period losing Andrejs Everitt, Jed Lamb, Shane Mumford and Jesse White after securing big-ticket Lance Franklin as a free agent from Hawthorn. The club also delisted Tony Armstrong.
Laidler adds some depth to a team that finished fourth in 2014.
He expressed his joy at joining the Swans on Twitter saying: "Stoked to be joining the @sydneyswans. Looking forward to the opportunity."
As expected, former Western Bulldog midfielder Daniel Cross also found a new club as a delisted free agent when he officially joined Melbourne.
After 210 games with the Bulldogs between 2002-2013, he made the move when the Bulldogs told him his time with them was up.
"I was there [at the Bulldogs] for 13 years, so it’s certainly going to be different to walk in through the Melbourne doors," Cross told Melbourne's website.
"It’s an exciting feeling for me. I’ve only known one way for a long time, so I’m excited by the challenge of building new relationships with players and playing alongside a whole bunch of new players, under a new coaching staff as well."