Grant succeeds Archie Kane, group executive director for Insurance and Scotland, who announced last week that he was retiring.
Grant will report to Antonio Horta-Osorio, the group chief executive, in his role as chair of the Scottish Executive Committee.
Horta-Osorio said he is delighted that Philip has agreed to chair the Scottish Executive Committee.
"We are one of the country’s largest employers and we recognize that we have a significant responsibility both to our colleagues and to the communities and businesses in Scotland that we support. Philip will be a great leader and ambassador for the Group in Scotland," Horta-Osorio said.
Apart from his Committee responsibilities, Grant will continue in his role as head of UK Private Banking reporting to Antonio Lorenzo, group director responsible for the Wealth and International division, Lloyds said.
Grant started his career with Bank of Scotland and has held a number of senior roles within the bank.
He is currently president of the Chartered Institute of Bankers in Scotland.