The US Federal Reserve has formally approved the Bank of America's purchase of investment bank Merrill Lynch, which was hard hit by the global financial crisis.

The bailout was announced in September at the same time that rival investment bank Lehman Brothers collapsed.

The deal makes the Bank of America the world's largest financial services company, with assets of more than $5 trillion and nearly 12 per cent of US bank deposits.

The central bank says the takeover will not harm competition.