Ros Micklem, who has been a Shelter trustee since 2014 and chairs its Scotland committee, has been elected to replace Myers, who was chief executive of the Royal Borough of Kensington and Chelsea when the decision was taken to refurbish Grenfell Tower.
Another trustee, Tony Rice, who is chair of an investment firm that is the major shareholder in a company involved in the refurbishment of Grenfell Tower, stood down at the same time as Myers.
Micklem is a former Scotland director at the Equality and Human Rights Commission and has a background in higher education, Shelter said.
She will step down from her role as chair of the charity’s Scotland committee in August when a new chair in Scotland is elected.
Ruth Hunt, chief executive of the equality charity Stonewall and a Shelter trustee since 2015, has been elected vice chair, the charity announced.
Joanna Simmons, a former chief executive of Oxfordshire County Council and a Shelter trustee for the past five years, has been elected chair of its audit, risk and finance committee.
All three appointments are for a one-year period, which is because the charity is understood to be using the opportunity presented by the changes to carry out a governance review.
The charity’s board has two vacancies after the departures of Myers and Rice, but does not plan to fill these until after the review is completed so it can establish what skills it needs.
Micklem said in a statement: "I feel honoured to have been elected to chair the board for the coming year. I’m really looking forward to working with the incoming chief executive Polly Neate and her team to build on what’s great about Shelter, encourage fresh thinking and develop a clear sense of direction for the years ahead."