The work and pensions secretary said Ruston Smith, a trustee director at Peoples' Pension, Standard Life's Jamie Jenkins and Pensions Policy Institute director Chris Curry will chair the probe.
British businesses have been automatically enrolling eligible employees into pension schemes since October 2012, with the smallest companies planning to stage the retirement initiative by April 2017.
The overhaul, part of the 2008 Pensions Act, is designed to "nudge" people into saving for their futures since workers can opt-out of the schemes.
Green, speaking at the Age UK conference in Westminster, revealed that more than seven million people have been enrolled into the scheme, with nine out of 10 people agreeing not to opt-out.
"By next year, 10 million people will be saving or saving more for their private pension," he said.
The senior Conservative also stressed that the new review would help the government "ensure" the automatic-enrolment scheme continues to work in the future.
"For me automatic enrolment symbolises how I see the relationship between welfare, the state, individuals and employers. The welfare state is no longer enough, what we need now for the 21st Century is a welfare system," he added.
Greens comments come after independent think-tank the Institute for Fiscal Studies (IFS) estimated that £2.5bn ($3.1bn) a year has been saved thanks to the automatic enrolment programme.
But pensions provider Aviva has called on the government to increase minimum contribution rates for workers and employers. The rates will eventually rise to 8% from employees and a minimum of 3% from their company.
Aviva has argued that this will not provide most people with a "good level of income" in retirement.
The pensions provider wants contributions to be frozen for four years until 2023, with worker and employer contributions "gradually" increasing towards 5% each between 2023 and 2028.
"By increasing the minimum auto-enrolment contributions, we can improve the retirement prospects of ordinary people," said Andy Briggs, chief executive of Aviva UK and Ireland.
"Automatic-enrolment has already proved hugely successful, but there is no time for complacency as we still face the challenge of people not saving enough for their retirement. So we need to build on the success we've had so far."