The 26-year old Australian international was given permission by the Premier League to sign a one-year deal with the Seasiders despite the transfer window closing.
Carney completed a medical and signed the deal on Tuesday but Blackpool held fears that the paperwork may have not been submitted on time.
"We got the e-mails back from FC Twente just before six so it was a mad dash to get them printed off and faxed over to the FA and Premier League," Williams told the club's official website. "Fortunately the confirmation came through on Wednesday morning and I was delighted to tell the gaffer and Carns that the move had been given the green light."
Carney added: "It has been a busy 24 hours but I am delighted it is done now and I am just looking forward to getting out there playing. The way Blackpool play suits me and I am looking forward to meeting the lads and getting started."