A landlord pouring $30 million into a makeover of a downtown Brooklyn storage building has signed a podcasting company as a tenant, part of a push to lure creative businesses to the area.

Gimlet Media Inc. has signed a 10-year lease to take nearly 27,000 square feet on the seventh floor of the Pioneer Building, said Craig Deitelzweig, managing director at Building and Land Technology, which owns the office property with Quinlan Development Group LLC. Gimlet will relocate from its Gowanus office, Mr. Deitelzweig said.

The...