Members of trade union Unite, working for seven major oil distribution firms, voted by 51% overall on a turnout of 69% to accept proposals, which include the introduction of an industry-wide accreditation, or 'passport', covering health safety and training.
Despite the overall vote in favour, members working in four of the seven firms voted to reject the proposals.
Neil Carberry, CBI director for employment policy, welcomed the news. He said: "It's good to see that, in the end, cool heads prevailed and the dispute was settled by negotiation.
"The employers involved made clear their commitment to addressing health and safety concerns."
But Unite warned the overall narrow 'yes' vote left the companies with no room for complacency. The union stressed fundamental problems remain in the industry with urgent action needed to halt the race to the bottom and bring stability and security to the supply of a vital commodity.
Unite assistant general secretary Diana Holland said: "This narrow vote in favour lifts the threat of strike action, but leaves the companies with no room for complacency. We look forward to the rapid implementation of the Acas proposals which include an industry-wide 'passport'. The progress made through negotiation is testament to the brave stance members have taken in the face of growing insecurity and attacks on their profession.
"The narrow vote in favour should be a 'wake-up' call for an industry riddled with deep seated problems. This is why we are writing to the Energy and Climate Change select committee urging them to investigate the instability in the industry.
"Francis Maude's calamitous intervention highlighted that this country runs on unstable, short fuel supplies. It is not a jerry can in the garage we need, but a review of whether the industry is structured in the national interest. We trust that energy secretary Ed Davey and other ministers will take a more constructive approach in helping us bring stability and security to a nationally vital industry."
The first meeting to take forward the implementation of the Acas proposals must be held before 1 June.
The consultative ballot involved over 2,000 tanker drivers working for Wincanton, DHL, Hoyer, BP, Norbert Dentressangle, Turners and Suckling.
