The disposal comes a decade after the bank was set up, with 55 per cent owned by Sainsbury's and 45 per cent by Bank of Scotland, which is now part of HBoS.
According to the retailer, both parties feel the revised structure is more appropriate because it reflects a shared commitment to growing the business in the long term.
The sale will give the grocer a profit of about£10 million to the grocer and the proceeds will be used for 'general business purposes'.
The board of Sainsbury's Bank will comprise eight directors: three from
Sainsbury's, three from HBoS and two from the bank.
HBoS retail chief executive Benny Higgins will become chairman for two years, after which Sainsbury's chief financial officer Darren Shapland will assume the role.
Along with Shapland, the Sainsbury's directors will be customer director Gwyn Burr and HR director Imelda Walsh.
Benny Higgins said: 'Sainsbury's Bank has strong customer loyalty. The
business has demonstrated it can acquire and retain customers very effectively.
There is significant potential to grow the business. We aim to do just that.'
Darren Shapland said: 'The bank's chief executive Rob Walker is streamlining the operational structure and developing a broader business plan.
'The sale of our 5 per cent for£21 million demonstrates the value of the bank and a 50/50 structure reflects the continued commitment of both shareholders.'