Ron Sandler, currently executive chairman of NR, will become non executive chairman.
Hoffman has been with Barclays since 1982 and has held a number of senior roles during this time including Barclaycard chief executive, chairman of UK banking and chairman of Barclaycard.
He has been an executive director of Barclays for the last four years and became group vice chairman in 2006.
Hoffman says: “This is an exciting opportunity for me. NR enjoys strong local roots and community support, an extensive customer base, and an extremely loyal set of employees who have been through a great deal recently.
“I am excited by the prospect of leading the company back to a position of strength, delivering our plan and returning NR to private ownership as a thriving, stable business.”
Sandler says: “This is a major step forward for NR and I am delighted that Gary will join the board as chief executive officer. His skills, experience and overall track record make him an outstanding candidate for the role.
“Gary further strengthens our executive team and he will provide the leadership to deliver our business plan and take the company forward. I look forward to working with him.”
Andy Kuipers, current chief executive officer of NR, will leave the company on August 31.
Of Kuipers exit, Sandler says: “Andy became CEO in extremely difficult circumstances and he has performed the role admirably during his time in office.
“On behalf of all at NR, I would like to thank him for his outstanding contribution to the company over 20 years of service. He has my best wishes for the future.”