Thickett has been at the magazine some 11 years, editing the red top title for the last five.
He joins the association alongside Sarah Wilde, who joined the BSA on June 30 this year.
Wilde has experience in financial services, fundraising and business development.
Paul Broadhead, head of mortgage policy, said: "I am delighted that Sarah and Robert are joining the team at the BSA.
"Both of them have worked in financial services before, during and after the financial crash of 2008.
"They have a sound knowledge and understanding of the regulatory, political and socio-economic changes and developments that BSA member’s experience.
"The housing market makes headlines daily and is one of the two main businesses for all 44 building societies.
"Together, BSA members serve millions of mortgage borrowers across the UK, accounting for over one in five new mortgage loans. These days all lenders operate in a constantly moving regulatory environment with changes emanating both from Westminster and Brussels.
"We also have a housing market which in recent months has seen some dramatic changes. I look forward to having Sarah and Robert on the team and wish them every success at the BSA."
