Very simply, economic growth is correlated with long term interest rates in the sense that interest rates are set according to the growth of the overall economy and GDP. If economic growth is weak, interest rates are set very low as a means of economic stimulus. If economic growth is too strong due to demand and the economy is overheating, interest rates are slashed.
The Federal Reserve alone determines interest rates, as well as the federal funds rate and the discount rate, through the Federal Open Market Commitee. Visit Federal Reserve System