BT Openreach chief executive Joe Garner is set to become the new chief executive of Nationwide.
Mr Garner will replace Graham Beale, who announced his intention to leave Nationwide earlier this year, next spring.
BT said it had begun the process of recruiting a new boss for Openreach, the company's fixed-line telephone and broadband network.
Mr Garner said the opportunity to become chief executive of "one of Britain's most important financial institutions" and service champions was too good to turn down.
Speaking about BT, he added: "In my view, it is BT's investment that has helped the UK to become one of the strongest digital economies in the world and I am proud to have contributed.
"Openreach is now poised to take the UK from a superfast to an ultrafast nation and I am confident it can achieve this as part of the BT family. I wish my successor at Openreach and everyone there and at BT all the best for the future."
He replaces Mr Beale, who has held the role of Nationwide chief executive since 2007 years and been with the building society for 30 years.
It is not yet clear where Mr Beale will head next, and it is believed he is still considering his options.
Commenting on the appointment, Nationwide chairman David Roberts said: "I am delighted that Joe Garner has agreed to join Nationwide, succeeding Graham Beale.
"Nationwide is the UK's largest mutual building society and our vision is to be the stand-out retail financial services provider in the eyes of consumers. As a member-owned organisation, our sole focus is to deliver exceptional products and services to our members at every stage of their lives.
"Mr Garner has an excellent track record in delivering outstanding service to customers across the financial services and retail sectors, and is a passionate advocate that financial services organisations should always put the customer first."