That appears to clear the way for four more countries to join the union.
The Cabinet accepted the compromise, opposed by anti-European members of the Conservative Party, at a lengthy meeting Tuesday morning.
Although Britain favors expansion of the community, Major had taken a hard line against proposed changes in decision-making within the community when it expands from 12 to 16 members, with the addition of Sweden, Norway, Finland and Austria.
The EU nations now vote on many issues under a system of "qualified majority voting," weighted according to population. Britain, France, Germany and Italy get 10 votes each; Spain, 8; Belgium, Greece, the Netherlands and Portugal, 5 apiece; Denmark and Ireland, 3 each, and Luxembourg, 2.
Any decision can be blocked by 23 votes.
Under the plan drafted this weekend at a meeting of European foreign ministers in Greece, the "blocking minority" on votes would be 27, but if there were at least 23 votes against any proposal then further talks among members would be required.
Britain and Spain had objected to proposals to raise the "blocking minority" to 27.
Major said he would have preferred a decision in favor of 27, but said Britain had won assurances from the European Commission that would help protect British interests.
EU members will meet to approve the rule changes on Wednesday. If approved, the last obstacle to the entry of Sweden, Norway, Finland and Austria, will have been removed.
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