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Under the terms of a "gentleman's agreement", Yugoslavia has agreed to give up the seat after serving one year, only half the usual two year term.
The understanding is the Philippines - the runner-up in the election - will then be elected to complete the term.
Today's vote at UN headquarters in New York ends a two-month deadlock over which country should replace Turkey on the Council .
Traditionally there are five permanent members on the council which each hold the power of veto, the United States, United Kingdom, USSR, China and France, and five other temporary members are elected for two years each.
Non-permanent members are elected according to their contribution to international peace and they are also meant to reflect a broad geographical distribution.
The seat which has now been taken by Yugoslavia was originally reserved for an eastern European representative.
Yugoslavia had the backing of the UK, nearly all European countries and most commonwealth countries, together with the Communist group and some Asian countries.
But, the United States, with solid Latin American support and some Asian backing, was supporting the Philippines' claim on the grounds Asia deserved more representation on the council.
Various attempts have been made to reach a decision. In total, members have been asked to vote more than 30 times over the past two months and a variety of compromise countries have been put forward. But none has reached the required two-thirds majority.
In today's vote, Yugoslavia finally received 43 votes, Philippines got 11 and Sweden and Finland took one each. Thirteen countries abstained and one vote was invalid, thus the two-thirds majority needed was 38 votes and Yugoslavia received more than this.
BBC correspondent F D Walker said: "It has certainly been eventful, this tenth session of the Assembly."
Earlier in the week, 16 new members were voted into the United Nations, including Italy, Spain, Portugal, Ceylon, Eire and also four new members from the Soviet bloc, Bulgaria, Romania, Albania and Hungary.
Only two members have been denied a place - Japan and Outer Mongolia were vetoed.
Yugoslavia did resign its seat on the Security Council the following year and the vacancy was filled by the Philippines.
A decision was taken in 1963 to increase the membership of the Security Council to reflect the increased membership of the UN.
It was decided that the 10 non-permanent members should be elected according to the following pattern: five from African and Asian states; one from Eastern European states, two from Latin American and Caribbean states, and two from Western European and other states.
The first expanded council with 15 menbers was elected in 1965.
Arguments continue to rage over representation on the Council and the power of veto.
The Security Council's main function is to maintain peace and stability. It can issue ceasefires, order sanctions and in extreme cases organise military action.
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