The Australian share market has closed at a two-month high as markets around the globe rallied on hopes for a coronavirus vaccine.

The S&P/ASX200 benchmark index finished up 99 points, or 1.81 per cent, at 5559.5 points, while the All Ordinaries index closed up 101.3 points, or 1.82 per cent, at 5658.8.

The Australian dollar was buying 65.46 US cents, down from 64.32 US cents at the close of trade on Monday.