It is the bank’s first major transaction since being bailed out by the taxpayer eight years ago.
Lloyds chief executive Antonio Horta-Osorio said MBNA, which holds assets of £7 billion, would be a “good fit” with the bank’s current credit card business.
The bank said its share of the UK credit card market would increase from about 15% to 26%. MBN will increase group revenues by £650m a year.
The price paid by Lloyds includes around £800m of acquired equity and assumes £240m for future PPI claims,
Lloyds said the MBNA deal would bring a “significant opportunity for cost synergies”.
There is said to be some concern in Chester, where MBNA’s UK business is based, that 1,700 jobs could be relocated to Lloyds’ other offices around the UK.