The bank said it had come to the decision to move the unit following a review, which found that it needed "significant technological investment" in order to continue operating efficiently, the BBC states.
Barclays therefore concluded that outsourcing the department's work to a "specialist third-party supplier" would provide a better service for customers, while bringing "significant" savings for the company.
The unit's new base will be in Stratford-upon-Avon. Job losses at its current offices in Windsor Place, Cardiff, will begin next Easter.
Responding to the announcement, trade union Unite described the move as a "bitter blow" for workers following the bank's earlier decision to close its First Plus division, which resulted in 300 redundancies.
Unite officer Steve Pantak added that the organization also has "grave concerns" about outsourcing the sensitive work of the unit, as handling deceased customers accounts requires "highly-trained staff".
Barclays currently employs around 120,000 people worldwide and has over 14.75 million retail and business customers in the UK.