Titcomb, who is chief operating officer and a board member at the Financial Conduct Authority (FCA), will take up the post from 2 March next year.
The regulator had been searching over a period of 18 months for a permanent replacement for former chief executive Bill Galvin.
Titcomb said: “The UK is currently undergoing a pensions revolution. With so much fundamental change, it is important that the industry is overseen by a strong, independent pensions regulator, focused on the issues within the sector, that is respected for its technical expertise and authoritative voice.
“I relish the opportunity of working with the regulator’s high quality team and with other industry stakeholders to ensure that the changes and new freedoms planned for the pension system deliver clear benefits for retirement savers.”
Welcoming the appointment, TPR chairman Mark Boyle said: “Lesley brings a wealth of regulatory and operational experience, at a time when The Pensions Regulator’s responsibilities continue to expand.
“Next year will see the introduction of new minimum standards and a charge cap for DC schemes, much greater freedom for members drawing a retirement income, new regulatory responsibilities for public service pension schemes and the roll out of automatic enrolment to small and micro businesses. I look forward to working with Lesley and colleagues at the regulator as we tackle these important challenges.
“I would like to thank interim chief executive Stephen Soper for his strong leadership during an extremely busy and challenging period, which has seen the successful implementation of the first phase of automatic enrolment and a number of landmark case outcomes for the regulator. Stephen continues to lead the organisation until March.”
The regulator has been searching for a permanent chief executive since last March, when Galvin announced he was stepping down, and reopened the application process last month.
Boyle joined TPR as chairman six months ago.