The Australian share market closed firmly higher on Wednesday, with stronger oil prices driving the index.

At the close of trade, the benchmark S&P/ASX 200 index was up 34 points or 0.59 percent at 5,772.10, while the broader All Ordinaries index added 33.7 points or 0.58 percent at 5,840.80.

Bolstered by a positive lead from U.S. markets and an upgrade of the International Monetary Fund's global economic growth forecasts, Australian investors looked to buy and higher oil prices meant it was the energy sector which was the day's best performer.

In the financial space, Australia's big banks strengthened, although the Commonwealth Bank remained flat (0.00 percent), Westpac Bank was up (0.71 percent), National Australia Bank up (0.44 percent) and ANZ (0.44 percent).

Mining stocks saw mixed results with BHP up (0.49 percent), Rio Tinto down (0.56 percent), Fortescue Metals down (1.78 percent) and Newcrest Mining up (0.46 percent).

The country's oil and gas producers surged with Woodside Petroleum up (1.29 percent), Santos up (0.74 percent) and Oil Search up (0.42 percent).

Australia's largest supermarket chains also rallied with Wesfarmers up (0.63 percent) and Woolworths up (0.69 percent).

While telecommunications giant Telstra gained (0.29 percent), the national carrier Qantas soared (0.97 percent) and biomedical firm CSL lifted (0.44 percent).