Peace is the chief executive of the British Property Federation, a non-executive director of the Planning Inspectorate and was made a CBE in 2008.
Cass is an architect, landscape architect and masterplanner. He has managed and delivered large-scale projects, including the Liverpool International Garden Festival, and contributed to a Parliamentary Select Committee on housing and brownfield land.
They replace Alan Barber OBE, who stepped down last year due to ill health, and Paul Morrell, who has served eight years, the past four as the deputy chairman of CABE.
Existing commissioners Joyce Bridges and Robin Nicholson will now be joint deputy chairmen.