In a speech at Northumbria University in Newcastle he also declared it would be equally misguided to think, if UK growth were to be near its longer-term trend rate, monetary policy should be returned quickly to a more normal footing.
Mr Miles' speech followed a move by financial markets to price in the first rise in UK base rates in the next 18 months. Base rates have stood at 0.5% since March 2009 .
The Bank of England's nine-strong Monetary Policy Committee last month declared that it did not intend to raise base rates from their record low of 0.5% at least until the International Labour Organisation measure of unemployment had fallen to a "threshold" of 7%. It is projecting this will not happen until 2016.
The new forward guidance on rates would cease to hold if the MPC thought it more likely than not that annual consumer prices index inflation, 18 to 24 months ahead, would be 0.5 percentage points or more above the 2% target, or if medium-term inflation expectations no longer remained sufficiently well anchored.
Figures published last month by the Office for National Statistics showed UK gross domestic product grew by 0.7% in the second quarter. This followed expansion of 0.3% in the first quarter, and contraction of 0.2% in the closing three months of last year.
Economists believe, based on business surveys, that the third quarter will also have seen significant growth. Mr Miles said: "For the first time in some years, the news on the outlook for economic activity in the UK over the past month or so has been overwhelmingly positive.
"Business surveys - of both current and future activity - look stronger and consistent with growth at least as high as what we used to think of as normal. Consumer confidence has moved up sharply. Hardly any indicator has failed to improve. This is all encouraging and very welcome.
"It is likely that the rate of the growth of the economy right now is at - and quite possibly above - the average rate in the 50 years up to the onset of the financial crisis that started in 2007."
However, he added: " This comes after a period of several years of virtually no growth; and those recent low-growth years came after a disastrous period in 2009 when output plummeted.
"So it would be spectacularly misguided to think that some signs of more normal growth mean that the economy is back to normal; and it would be equally misguided to think that, if growth were to be near trend, monetary policy should be quickly returned to a more normal setting."
Mr Miles cautioned that recent encouraging signs of growth might not prove to be durable, while highlighting his belief that they would be.
He noted the economy had been operating far short of its potential, and said the amount of slack was almost certainly large enough to mean a sustained period of above-average growth would be needed to remove it.
Mr Miles added: "The reason I think guidance is helpful now is that it reduces the risk that a recovery that is still somewhat embryonic is not smothered by the anticipation that a tightening in monetary policy is imminent."