Low interest rates often spell trouble for mortgage servicers, which can lose business as homeowners refinance their loans.

Michael Nierenberg, chief executive officer of New Residential Investment Corp., plans to finesse the problem by buying assets from bankrupt Ditech Holding Corp. and offering customers cheaper rates himself.

New Residential, managed by Fortress Investment Group LLC, signed a tentative agreement to pay $1 billion for Ditech’s mortgaging servicing rights that cover $63 billion in loans, and to take over some Ditech office spaces and employees, the companies said June 18.

The deal has former Bear Stearns Cos. colleagues on each side:...