Mackay is to leave GSK at the end of 2023 and become an independent non-executive director of Schroders next year.
Mackay is chief financial officer at pharmaceutical company GSK and is a former group finance director at HSBC Holdings.
Robinson is general counsel of asset management company Vanguard, and previously held positions at Deloitte, American Express and Citi.
Chair Paula Rosput Reynolds says the appointments “bring new depths of UK and US business and regulatory experience to the board”.
The former UK minister for trade and investment was once the youngest FTSE 100 CFO and is a former BT group CEO.
Sir Peter Gershon will be succeeded as nomco chair by non-executive director and chair designate Paula Rosput Reynolds from 1 January.
Rick Haythornthwaite is to step down as Centrica chairman, while senior finance chiefs are set to leave GSK and National Grid.