In a statement, TSB said Cooper brings "the right range of skills and experience needed as the bank implements its growth strategy and continues to evolve to meet customer expectations in the context of a changing banking landscape".
Cooper was previously director and general manager of Baycorp Holdings (NZ), and spent a decade at payments giant American Express. She starts her new role on July 23.
The hire comes after a lengthy search period. Former boss Kevin Murphy announced his retirement in November last year and stood down in February.