The Welsh club clinched a place in the top flight on Tuesday night for the first time in 51 years following a 0-0 home draw with Charlton Athletic.
Malaysian businessman Tan, who has injected over £60m into the club, is delighted with the achievement and will now plan the way forward with Mackay.
"It's a great feeling," Tan told Sky Sports News. "It's about time right for Cardiff City?
"I think we have to strategise how we stay there for a long, long time. We have to do a lot of thinking.
"Hopefully we don't have to spend too much, but Cardiff have waited for 51 years, so this great. I'm very happy that Malaysia helps to contribute to this.
"I think Malky is a fantastic manager. We work along very well and we have a great working relationship.
"I've a lot of respect for him and he has a lot of respect for me. It's a great mutual relationship."
Tan caused controversy last summer when he changed Cardiff's home colours from blue to red, but after the club endured several near misses in the bid for promotion he said: "Lucky red, you know."