The Scot agreed a three-year deal in the Welsh capital, just 24 hours after being given permission to hold talks by a reluctant Watford board who at first rejected an official approach from the Bluebirds.
Cardiff have had to pay an undisclosed fee to his former employers, for whom Mackay only signed a new three-and-a-half-year contract in March.
Speaking at his unveiling, broadcast live on Sky Sports News, Mackay said: “I see a club with massive ambition, an infrastructure that is exciting, a beautiful stadium, great training facilities and a club that wants to go places.
“I know the division and I know the type of players we want.
“Everyone goes into the race to win it and we will be one of the clubs trying to win it.
“Cardiff are a team that have done very well over the last few years.
“Two play-offs and a Wembley final appearance can’t be criticised.
“It’s well documented the finances we’ve been working under at Watford. Watford over the last couple of years have fought hard under the restrictions. But coming here gives me an opportunity to challenge at the top of the table.”