The result of the vote paves the way for the firms' management to submit to the European Commission their proposals for creating the world's largest professional services practice. Besides the 8,500 partners, it would have 135,000 staff around the globe and total revenues of more than $13bn (pounds 7.6bn).
The plans are already being scrutinised by regulators in other parts of the world, including the United States. However, it is understood that the European competition authorities wanted to wait until the ballot of partners had been completed in case there were any changes to the original proposal.
With the Brussels regulators likely to consult with the UK's Office of Fair Trading and other parties, both firms are resigned to the inquiry taking several months.
Meanwhile, the timetable of the proposed union of KPMG and Ernst & Young has slipped. The two firms, which in October announced plans to create a combined firm even bigger than that proposed by Coopers and PW, will not ballot their partners until early next year.
The intervention by KPMG and E&Y is known to have irritated Coopers and PW on the grounds that two combinations would represent a much greater consolidation in the accountancy market than a single merger and might be seen as a bigger threat to competition.
However, all four firms have stressed that the markets in which they operate are complex. While observers have expressed concerns about competition, standards and costs, the managements emphasise that in management consultancy and corporate finance, accounting firms face many competitors.