Bester, who was group director and chief executive of the commercial banking division at Lloyds until 2017, will succeed Liam Coleman.
Coleman announced he was stepping down in June after less than 18 months in the role.
Bester will lead the Co-op Bank in its quest to turnaround the business following a US$900mln rescue deal with US hedge fund creditors last year after the bank discovered a £1.5bn black hole in its finances in 2013.
He was once viewed as a possible candidate to become the next Lloyds chief executive, having played a vital role since 2012 in helping to revive the bank following its government bailout during the 2008-09 financial crisis.
Co-op Bank chairman Bob Dench said Bester was the perfect candidate to take the helm of the lender as it seeks to become a “sustainable profitable bank”.
“He is a first class business leader with the experience, drive and intellect required to lead the organisation forward at a key point in its turnaround journey,” Dench said.
Bester, who was also chief operating officer for consumer banking at Standard Chartered (STAN.L) prior to Lloyds, will join the board on Monday to start the transition of responsibilities from Coleman.
“Over its recent history, the bank has been through a period of great change and uncertainty and I look forward to working with the teams to return the business to its former strength,” Bester said.