The Edinburgh-born midfielder, who also played for Hearts and Tottenham, died aged 80 after suffering from both dementia and Parkinson's disease.
Mackay captained Derby under Brian Clough and later managed the club, leading the Rams to the Division One title in 1975.
His widow Isobel said the honour was "brilliant" and "well deserved".
She said: "I am very proud and I am sure he would have loved [the statue] and given it a thumbs up.
"The club have done a tremendous job, it is so lovely to sit in the Dave Mackay Lounge."
John Vicars, Derby County's chief operating officer, said: "I'm delighted that we have been able to pay tribute to Dave Mackay and, as such, remember his contribution to Derby County in this way."
Andy Edwards, who was commissioned to produce the memorial, said: "To play a part in this permanent tribute... is an eternal blessing for me."
Mackay joined Derby in 1968 and helped the side win promotion to the top flight the following year.
He returned in 1973, replacing his former boss Brian Clough in acrimonious circumstances, and guided the team to the Division One title.
Mrs Mackay said: "He was so proud to achieve that after all the turmoil that was there when he joined as manager.
"He was the only person then that could have done the job and got the ship out of stormy waters."
Mr Mackay's funeral was held in Edinburgh in March and was attended by football legends Sir Alex Ferguson, Denis Law and Pat Jennings.
A statue has been unveiled at Derby County's iPro Stadium of their former player and manager, Dave Mackay.