The Dow Jones Industrial Average rose 0.8% to 17,050.7 points.
The other main US indexes also gained, with the S&P 500 up 0.9% at 2,013.4 and the Nasdaq 0.4% higher at 4,810.7.
It was the highest close for the S&P in seven weeks as the Fed waited for more information about the US recovery before raising rates.
The minutes "were certainly not suggesting the Fed may raise its rates anytime soon", said Chris Low, chief economist at FTN Financial.
Energy stocks rose more than the rest of the market as the price of oil continued to recover, with Chevron adding 2%.
Brent crude was up 0.4% at $53.28, and US oil was 0.5% higher at $49.66, helped by a weaker dollar.
Netflix jumped 6% after the video streaming company said it would raise its prices in the US.
Avon was the biggest riser on the S&P, adding almost 14%,
EMC rose 4.7% after Reuters reported that Dell was in talks to buy the data storage company.
(Close): Wall Street finished higher on Thursday after the minutes of the Federal Reserve's September meeting were published.