Woodall stepped down from her role at the FCA in December last year. She was previously director of mortgages and consumer lending at the regulator.
Woodall replaces Institute of Customer Service chief executive Jo Causon who served on the committee as an independent member since it was created in 2015.
Aegon IGC chair Ian Pittaway says: “Linda will bring fresh insights and challenges to our IGC and will make sure we continue to focus on broader regulatory developments in defining ‘value for money’.”
Woodall adds: “We’re reaching an interesting juncture as rising pension contributions create a huge test for auto-enrolment and pension freedoms change peoples’ attitudes towards retirement income.
“IGCs need to continue to challenge and ensure that members receive good value for money and good outcomes from their workplace pensions.”
It is understood Woodall has also pick up a role on the board of compliance consultancy Huntswood.
Woodall joins a number of former senior FCA staff who have picked up director roles within the industry soon after they left the industry.
Former chief executive Martin Wheatley became an adviser for a Hong-Kong based hedge fund, his successor Tracey McDermott joined Standard Chartered, and pensions director Nick Poyntz-Wright took a non-executive role at closed-book provider Phoenix.
A February report by pressure group ShareAction criticised independent governance committees and challenged them to do better.
The report said independent governance committees at big-name pension providers are failing to safeguard the interests of savers and that the FCA must take action.