David H. Stevens, who last week said he would step down as commissioner of the Federal Housing Administration, will be named the next chief executive of the Mortgage Bankers Association.

Mr. Stevens emerged as a key adviser on housing-finance policy during a two-year stint in the Obama administration. At the MBA, he will succeed John A. Courson, who is departing in an unexpected shake-up at a trade association that has been through a tumultuous period.

Mr....