Lloyds, which owns the Halifax bank, said it wants to boost profits by expanding its consumer lending business.
Lloyds said the MBNA deal would bring an opportunity for "significant cost synergies", saying it expects to make savings of £100m a year, about 30 per cent of the credit card firm's cost base in 2015.
The banking giant has been implementing a restructuring plan and in October this year confirmed that more than 1,200 jobs would be lost. The cuts are part of the 9,000 job losses the bank first announced in October 2014.
A spokesman for Lloyds said it was too early to say whether there will be any job losses following the deal.
"The cost synergies will be achieved through the consolidation of IT infrastructure. MBNA's systems will be moved to Lloyds' systems," he said.
"On jobs, it's too early for us to say."
Analysts said the deal will increase Lloyds' profit and reduce its reliance on mortgage lending.
The move represents the first major acquisition for Britain's biggest mortgage lender, which is part-owned by the Government, since it was bailed out during the 2007-09 crisis.
Lloyds said the deal, which is expected to complete in the first half of 2017, includes around £800m acquired equity and assumes £240m for future claims for mis-sold loan insurance (PPI).
Analysts said the deal is a good use of the bank's excess cash, but warned it carried some risks given Britain's uncertain economic outlook following the country's vote to leave the European Union.
Gary Greenwood at Shore Capital said: "The anticipated financial performance and shareholder value creation that is expected to be generated by this transaction is impressive, in our view, and suggests a better use of capital than simply returning it to shareholders.
"That said, Lloyds will be broadly doubling up its exposure to credit cards at a particularly benign point in the bad debt cycle and ahead of a potential slow-down in the UK economy once the terms of the UK’s exit from the EU are reached.
"While there is some latitude in the financial metrics to absorb potentially higher impairments, the risk cannot be ignored. In addition, we see limited scope for organic growth given the high post transaction market share and attention such growth may attract from the competition authorities."
Antonio Horta-Osorio, group chief executive of Lloyds, said MBNA is a "good fit" with the bank's current credit card business.
He added: "The acquisition, funded through strong internal capital generation, increases our participation in the expanding UK credit card market with a multi-brand strategy and advances our strategic aim to deliver sustainable growth as a UK focused retail and commercial bank."
Lloyds said it is confident of being able to deliver a progressive and sustainable ordinary dividend in 2016, but Mr Greenwood said the bank might reconsider its special dividend promised for the end of the year in order to fund the deal.
The banking group said MBNA, which holds assets of £7bn, would deliver strong financial returns and bolster its position in the UK prime credit card market.
The deal will provide a £650m a year boost to Lloyd's group revenues, while enhancing the bank's group net interest margin by around 10 basis points per year.