The 23-year-old was at Saturday's goalless draw with Everton as he tied up a move for a fee believed to be in the region of £2million on a four-year contract.
Mackay said: "We have signed Kevin Theophile-Catherine from Rennes today [Saturday].
"He is a good defender, he is someone we have tracked over the last year in France. He is someone who has pace, is aggressive and has good experience in the French top division, so he is someone we feel will be a good addition to our squad."
The move takes Cardiff's summer spending through the £30million mark after the acquisitions of Gary Medel, Steven Caulker, Andreas Cornelius, John Brayford, Simon Moore and Maximiliano Amondarain.
Having made his seventh summer signing by bringing in the former France Under-21 defender, Mackay still hopes to bring in more new faces ahead of the transfer deadline.
He said: "We're still trying. If there's something else that comes up over the next couple of days we'll work hard to try and do something.
"But like anything there's competition and the people we bring in have got to add (quality) to the squad."