The defender, 24, completed his move on Thursday, signing a two-year contract at Gresty Road.
Thordarson is thrilled with his first new acquisition of the summer, especially after worrying that a rival club may try and hijack the deal.
"I was concerned that someone was going to come in and try to nick Patrick because he is a decent player and has the right attitude to become better," Thordarson told the club's official website. "But things moved really quickly on Thursday, faster
than anyone expected, and I am delighted to have signed him.
"He was recommended to me in the winter and I have been keeping an eye on him and have had updates on his progress. I have been able to go and watch him as well.
"He is quick, strong and aggressive and he is a good age at 24, that is important. He is desperate to do well and he will be a good signing for us and will be an asset for the club."