That is debatable. Raising rates was necessary, but he went too high and far too long.
Volcker raised rates because Reagan wanted to strengthen the dollar. The devaluation of the dollar in the early 1970's was the real catalyst behind all the inflation we had (see the Bretton Woods accord). Other factors were panic by politicians which led to price controls and over regulation of the oil market.
The real long term cure for inflation was the economic growth that resulted from Reagan's policies. That's right, economic growth is deflationary, contrary to what the central bank and politicians would have you believe. Your belief is necessary for you to allow them to micromanage the economy.