Cardiff issued a statement early on Friday afternoon confirming Mackay's departure, leaving coaches David Kerslake and Joe McBride to take charge for Saturday's clash with Sunderland.
The statement read: "The Board of Directors at Cardiff City Football Club have today relieved Malky Mackay of his duties. A new first-team manager will be appointed and announced in due course."
Tan subsequently released a personal statement, adding: "There has been a good deal of publicity generated by and about Mr Malky Mackay over the last few months.
"Indeed far too much dirty linen has been exposed to the public gaze. But, I stress, not by me. Indeed, I have deliberately not responded to this, hoping that the Club can be judged on its football rather than personalised arguments about who said what to whom.
"I have, however, regretfully concluded that it is no longer fair to the Club, its players, its fans, or the public more generally, for this uncomfortable state of affairs to continue. Cardiff City Football Club means far too much to us all for it to be distracted by this."
Early reports suggest that former Manchester United striker Ole Gunnar Solskjaer, in charge of Norwegian club Molde, will be among those targeted by club chairman Mehmet Dalman with a view to taking the reins, with Cardiff currently just one point above the Premier League relegation zone.
There was a significant reaction in Turkey, where the agent of experienced coach Yilmaz Vural appeared confident his man was in the running to land control of the Welsh club.
Muzzi Ozcan said previously via Twitter: "The story is coming to a [sic] End in Wales and a new story will be born ... The next 48 hours will be explosive!"
When news of Mackay's sacking broke, he added: "New page has been turned over as I said .... Wish the best for MM."
Vural has previously managed several clubs in his homeland and was most recently in charge of Elazigspor, but quit his post in May.
Malaysian owner Tan has courted controversy several times since purchasing a controlling share in the club back in 2010.
Large sections of City fans took exception to his decision to change the club's colours from blue to red, and he then fired Mackay's head of recruitment Iain Moody without consulting the Scot.
Last week, Tan issued an ultimatum to Mackay insisting that if he failed to tender his resignation, he would be sacked - prompting around 200 Cardiff supporters to launch a protest ahead of the 3-0 Boxing Day defeat to Southampton at the Cardiff City Stadium.
Mackay, 41, was appointed Cardiff manager in June 2011 and having guided the team to the Championship title last year, leaves after 125 games in charge with a win rate of 43%.
Initial shows of betting made 40-year-old Solskjaer the favourite for the job at 4/6, with Sven-Goran Eriksson second-favourite at 9/2, Vural at 5/1 and Tan backed into 20/1.