Lucas Silva is unlikely to join Real Madrid in January with the Spanish giants not planning to make any transfers.
Ravel Morrison has returned to parent club West Ham from Cardiff City on compassionate leave.
The defender, 21, left Tottenham for the newly-promoted side on a four-year contract for a fee in excess of £8m.
Caulker, who scored on his full England debut against Sweden in November 2012, said conversations with Mackay convinced him to leave White Hart Lane despite 26 starts in all competitions last season.
"His influence was massive," Caulker told Sky Sports News. "I spoke to Malky a couple of days ago and everyone's given him a glowing reference, so I'm looking forward to working with him.
"As soon as I heard about the move, I was really excited to come, hopefully play a lot of games and have a good season.
"Regardless of what team you're at you have to work hard and there's good competition for places as I've seen this morning. I'm going to work hard and I'm looking forward to the new challenge."
The move to last season's Championship winners sees Caulker return to south Wales following a loan spell with Swansea in 2011-12, also recently promoted at the time, with the prospect of a derby match in the Premier League already an exciting one.
"I enjoyed my time in south wales last time around and the people are great. I'm looking forward to the Swansea match, it'll be a massive derby."