The price of a barrel of Brent crude climbed close to $58 overnight, its highest level since July 2015, before edging back a little to above $56.
Oil prices had already been lifted after a deal reached a couple of weeks ago by the Saudi-dominated OPEC cartel to cut production by 1.2 million barrels per day from January.
That deal was the first of its kind since 2008.
A further deal over the weekend brought in producers outside OPEC – including Russia – who agreed to cut output by 558,000 barrels per day.
Fawad Razaqzada, technical analyst at Forex.com, said: “Make no mistake about it – this historic agreement is a game changer.”
Higher oil prices are likely to feed through to petrol price increases, ultimately pushing up inflation, but will also ease pressure on the beleaguered North Sea oil and gas industry.
The production cuts, to take effect from January, are expected to see the global oversupply of oil shift to a shortfall – pushing up the price.
Oil producers are acting because a glut of oil swilling around world markets – at a time of sluggish demand – has weighed heavily on the crude price.
Analysts at Bernstein said: “Once cuts are implemented at the start of 2017, oil markets will shift from surplus into deficit.”
Despite the latest rises, the price of a barrel of Brent crude remains 50% lower than its level in mid-2014.
A higher oil price will pose concerns for UK motorists facing a rising cost of filling up their tanks.
They face a double impact because the recent slump in the pound will make imports including oil – which is priced in dollars – more expensive.
But an upturn in the oil market will ease some of the pressure on the North Sea oil and gas industry which has shed thousands of jobs amid the severe price downturn.
UK-based oil giants BP and Shell – mainstays of many British pension funds – stand to gain, along with a raft of companies providing services to the industry.
Shares in both BP and Shell rose by 1.5% in Monday trading.