McDermott, who starts her role on 20 March, will report to CEO Bill Winters and will be based in London.
She will replace Steve Atkinson, currently group head of corporate affairs, in an expanded position – her job title will be group head, corporate, public and regulatory affairs. Atkinson will take a new role as Winters' chief of staff.
McDermott was acting CEO of the Financial Conduct Authority, the UK’s financial regulator, from September 2015 until June 2016.
Before this she held several senior roles at the FCA, including director, supervision and authorisations; and director, enforcement and financial crime. She was also a member of the board of the FCA from April 2013.
McDermott was also a member of the Financial Policy Committee of the Bank of England. She recently became a CBE in the Queen’s Birthday Honours list for services to financial services consumers and markets.
Winters said: "Tracey has played a critical role in shaping and changing behaviours in the UK financial sector. Her strong leadership skills, together with a combined experience of bank supervision, regulation and policy development is outstanding, and she will play a critical role in further enhancing our relationships with regulators and policy makers."
McDermott said: "Standard Chartered operates in some of the most exciting and dynamic markets in the world. The opportunity to join the bank at this critical point in its history, and in a time of global change, is one which was too good to miss. I am looking forward to working with Bill and the team to help continue the group’s transformation."
Standard Chartered employs around 84,000 people and is listed in London, Hong Kong and Mumbai. It operates in more than 70 countries.
The company has recently seen a lift in its share price, with some traders seeing at as a good bet amid the falling value of the pound, and reports that it will resume dividend payments.