The Department for Work and Pensions is believed to have picked one of its existing board members to replace Lady Judge, who is stepping down after six years.
Wagner retired from his main role as director of human resources in 2009 and joined the PPF’s board in 2011.
Lady Judge was appointed chairman of the pensions lifeboat in 2010 and she was given a second three-year term in 2013.
She was previously chairman of the UK’s Atomic Energy Authority between 2004 and 2010.
The appointment comes as the PPF is contending with crises at BHS and Tata Steel.
The PPF’s biography of Wagner notes: “Arnold has a strong interest in pensions, including defined benefit pension schemes.”