Mackay declared that he was delighted to bring in the experienced midfielder, with the deal 95% finished as the final paperwork is formalised by both parties.
He told Wales Online: "He was our guest here today. We are 95% there in terms of making him a Cardiff City player. There are still some details and documents to be ironed out before we finalise the deal. But I am absolutely delighted to secure his services.
"He was one of the top midfielders in La Liga last season and is an experienced international with more than 50 caps for Chile. He has played for Boca Juniors and Sevilla, so has a very good pedigree.
"He's a combative defensive midfield player, the sort we felt we required for the Premier League. We have been on the lookout for a player like Gary for a while."
The 25-year-old was linked with a switch to Everton earlier this summer, but Cardiff have moved first to talk terms with the midfielder.