Mackay, who joins the firm from Dundas and Wilson, has more than 35 years' experience of advising major financial services organisations.
He has specialised in financial services work for insurance companies, banks, building societies, asset management companies and other institutions, as well as dealing with the legal aspects of all types of retail financial products.
Burness has praised his "first-class insight into the challenges these businesses face, both at boardroom level and operationally, and how to tackle these on a practical basis".
Mackay is involved in advising clients on the effects on financial services businesses in the event of a Yes vote in the independence referendum, a result likely to boost the corporate legal profession, at least for the duration of what are expected to be lengthy negotiations.
Philip Rodney, Burness's chairman, said: "Financial Services is a sector which we see as continuing to drive the Scottish economy. Burness Paull has established a very strong reputation, acting for blue-chip clients such as Standard Life, Alliance Trust, Aegon, RBS, Lloyds Banking Group, Scottish Building Society and First State Investments.
"We have long regarded Philip as the leader in this field. His recruitment is an important component in achieving our aspiration to have the dominant financial services practice in Scotland."
Mackay said: "I am excited to be joining Burness Paull. It is a great opportunity to play a key role in helping to develop a financial services practice with a truly market-leading position in Scotland."