He succeeds Stephen Noakes, mortgage director for Lloyds Banking Group, who has been chairman for the last year.
McDonald said: “MMR made 2014 a huge year of change for the industry and we can feel proud of what has been achieved.
“We still face plenty of challenges in 2015 and I look forward to continuing the work the CML has done under Stephen Noakes as chairman to improve our customers’ experience of buying their home and managing their mortgage.”
McDonald will be supported by two deputy chairmen – Andy Gray, managing director of mortgages, Barclays Bank and Peter Hill, chief executive, Leeds Building Society.
McDonald joined RBS in 2010, when he was appointed director for home lending and in 2014 became managing director of products.
Moray also worked in lending businesses in Australia with Citibank and ANZ, and Spain and Portugal with BBVA and GE.