BADA will use the funds raised - the amount is undisclosed - to invest in boosting services for its 330 members and to buy new headquarters in time for the association's centenary in 2018.
In December the association will relocate to offices in Southwark for a year, with a view to purchasing a property in London in the longer term.
"It's clear we've got momentum in our modernisation programme and the building [20 Rutland Gate] was not appropriate for a progressive organisation," said Marco Forgione, the BADA's recently appointed chief executive. "Investing in Rutland Gate would have yielded diminishing returns as we continue to modernise."
"Secure the Future"
BADA have been at the property for more than 50 years and currently occupy two of the four floors they own in the seven-floor building. The remaining three floors accommodate leasehold apartments, which have also been sold.
Forgione said the association would invest the receipts "to secure the future of the association and ensure we are a viable organisation for another 100 years".
He added that some of the funds would go towards developing "a whole range of services and resources" for members, including help with digital marketing and business development.
According to annual returns filed with Companies House in July 2015, the BADA has a turnover of £334,000.
Rutland Gate was built over a period of more than 20 years in the late 1830s and '40s by property speculator John Elger and builder John Tombs, on the site of Rutland House, an aristocratic mansion.
Though the association is not disclosing the sale price it achieved, properties in this part of Knightsbridge the market frequently change hands for eight-figure sums.