Asda, Sainsbury's and Morrisons said they will cut the price of their petrol and diesel by up to 3p per litre.
The price change will come in at Asda stores on Thursday November 15, Morrisons on Friday November 16 and Sainsbury's on Saturday 17.
It is Asda's third petrol price reduction in less than three weeks, bringing the cost down by up to 8p per litre.
RAC fuel spokesperson Simon Williams said price cuts have been "an extremely long time coming" with petrol and diesel reaching a four-year high in recent months.
He went on: "There is finally some respite for hard-pressed diesel drivers from seemingly never-ending price rises with a sizeable but very much warranted price cut.
"The cost of buying petrol on the wholesale market has dropped like a stone so we should be looking for at least 5p to come off the average price of unleaded at the pumps.
"We believe Christmas has come early for fuel retailers across the board this year as they have been reaping the benefits of some of the biggest margins on fuel the RAC has seen in almost four years."
Over the past six months, the cost of filling up a typical 55-litre family car that runs on petrol or diesel has risen by around £6.
The average cost of petrol at UK filling stations dropped by just over 1p per litre in the past week to £1.29, according to Government figures.
Owners of diesel vehicles have been hit by price rises for 19 consecutive weeks, reaching an average of £1.37.
Where are there Asda, Sainbury's and Morrisons petrol stations in Leeds?
Leeds City Centre LS11 5BJ
Leeds Beeston LS11 8AG
Leeds Killingbeck LS14 6UF
Leeds Middleton LS10 4TQ
Leeds Morley LS27 0BP
Leeds Pudsey LS28 6AR
Dewsbury WF12 9AE
Leeds White Rose Centre LS11 8LS
Leeds Colton LS15 9JA
Rawdon Apperley Lane Local LS19 7BZ
Dewsbury WF12 8EB
Wakefield Marsh Way WF1 1QQ
Wakefield Ings Road WF1 1RS
Leeds Hunslet LS10 2AU
Leeds Kirkstall LS5 3AU
Leeds Bramley LS13 4DN
Leeds Morley LS27 9BG
Leeds Yeadon LS19 7PP
Heckmondwike WF16 0HL
Wakefield WF2 9BY
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