Speaking at the annual Mansion House speech, Mr King gave his final speech before his retirement.
The Bank of England Governor will be leaving the Bank in July when new Governor Mark Carney will take over.
On monetary policy, Mr King said he was aware interest rates were at "unsustainably low levels" and that this could not continue indefinitely. But he warned a rapid return to higher rates could damage households, companies and financial institutions.
"The challenge in returning to normality is not so much managing market expectations when that eventually happens, important though that is, but in creating the economic conditions in which it is sensible to return to more normal levels of interest rates," he said.
He said he was pleased with Mr Carney's appointment and felt he was leaving behind a "strong, independent, much-changed Bank".
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Mr King said: "The lessons of recent years have been learnt and it is up to us all to remember them. The test of our monetary arrangement is to see them work successfully under new leadership, none of whom were present at the creation. No doubt some things will change. No doubt some things need to change.
"After all one does not change an institution in order to set in concrete. A successful institution, just like the City as a whole, always adapts to new circumstances. I know the Bank will continue to do that under Mark's leadership."
It was also announced by Chancellor George Osborne at the same dinner that Mr King would be made a life peer for his services to finance.
Mr Osborne said: "You have been the original thinker who has taken Britain on the journey that began with inflation targeting, to monetary independence and now to the far-reaching reforms to prudential regulation and financial oversight.
"I can think of few people who have done more to shape our public discourse in the last 30 years and you have done so with integrity, intelligence and patriotism."

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