Mackay, 60, will be retiring next year after serving as GSK's finance chief for nearly four years, following an eight-year stint as group finance director at the bank HSBC.
Register now for FREE unlimited access to Reuters.com RegisterBrown, also 60, will join GSK in April and take up the job in May.
She also served in several finance roles at AstraZeneca (AZN.L), which last year also appointed a female CFO, Aradhana Sarin.
With Emma Walmsley as GSK's chief executive officer, Brown's appointment also creates a rare, all-female top management at a blue-chip (.FTSE) British company and a global pharma major.
Brown will receive an annual base salary of more than 900,000 pounds at GSK, the company said.