The benchmark S&P/ASX 200 Index and the broader All Ordinaries Index each added 1.1 per cent on Monday, to 5361.8 points and 5349 points respectively. The rally followed a horror week in which the benchmark index wiped out 2.75 per cent, falling below the level where it started the year.

Local shares rose on Monday after major markets in the United States, the United Kingdom, and Europe all lifted in response to increased global stimulus. Asian markets were stronger in the afternoon session.

The People's Bank of China surprised the market by cutting its benchmark interest rate by 0.4 percentage points. It was the first cut since July 2012. Later on Friday, European Central Bank president Mario Draghi said it was preparing to broaden its stimulus to beat low inflation, renewing expectations for a new round of quantitative easing to support global liquidity.

"The PoBC decision is undeniably good news for Australian miners and other stocks with direct exposure to China's economy," Pengana Australian Equities Fund investment analyst Mark Christensen said.

"And while easing from the ECB will have less direct impact on Australian company earnings, it delivers a nice kicker that will help support global growth," Mr Christensen said.

Resources giant BHP Billiton posted its biggest daily jump in almost three years, up 3.8 per cent to $32.90. The company told an investor meeting of plans to cut $US1 billion of costs in the 2016 financial year, and unveiled a management shake-up before next year's spinoff of non-core assets.

"The investor presentation again highlighted differentiation against peers who cut progressive dividends, so we expect BHP to move heaven and earth by reducing costs and capex further, before any change to the dividend policy," Citi resources analyst Clarke Wilkins said.

Mining was the best-performing sector, up 3.3 per cent, as the news of looser monetary policy in China provided some relief for the iron ore price outlook.

Rio Tinto, Australia's biggest iron ore miner, gained 3.4 per cent to $58.30. Fortescue Metals Group, the third-largest exporter of the steel-making commodity, jumped 10.8 per cent to $2.98 – its biggest daily spike in more than two years. Traders said many investors were closing short positions.

The spot price for iron ore landed in China was 0.9 per cent weaker late on Friday at $US70.31 a tonne, with futures traders tipping a moderate rise overnight.

As the biggest miners rallied, the big four banks were also stronger. Westpac Banking Corporation added 0.8 per cent to $32.50, while Commonwealth Bank of Australia and National Australia Bank each rose 0.4 per cent to $80.42 and $32.40 respectively.

ANZ Banking Group added 0.2 per cent to $31.87, as Bell Potter's Charlie Aitken upgraded it to a "buy" given the bank's south-east Asian business is set to benefit form lower interest rates in China.

Among other big bluechip industrial stocks, Telstra Corporation was unchanged at $5.65. Woolworths lost 0.6 per cent to $31.41, while Wesfarmers, owner of Coles, jumped 1.9 per cent to $42.35.

ALS Ltd, a laboratory that provides testing services to the mining industry, was the best-performing stock in the ASX 200, spiking 17.9 per cent to $5.28, after beating its interim profit guidance for $64 million with a reported $67.7 million. While better than forecast, the half-year result was still a 33 per cent drop from the year before.

Credit reporting agency Veda Group dropped 3 per cent to $2.29 as Goldman Sachs gave notice of ceasing to be a substantial shareholder.

On Tuesday, the local focus will be on the $5.68 billion float of Medibank Private, the largest government privatisation to come to the ASX since the $14 billion partial float of Telstra in 1997.

"The final price in the broker firm offer is pushing the boundaries of good value but we have taken a stake with a long-term view and expect it to do quite well," Australian Ethical portfolio manager Mason Willoughby-Thomas said.