The allies carried out an international (de facto British-led) occupation of Istanbul from 1918-1923. This was in line with agreed-upon war aims and the Treaty of Sevres which would have made Istanbul, and perhaps most importantly the straits, international territory.

European willingness to enforce the terms of Sevres, which called for extensive occupations of most of modern Turkey, declined dramatically during those years. The Franco-Turkish War (1918-1921) resulted in the French abandoning their claims to Cilicia (a vaguely-defined but quite large territory in south-east Turkey). Italy was mostly interested in ensuring that its rivals didn’t benefit. Britain’s support to Greece in the Greco-Turkish War was unpopular even among the British cabinet, particularly given the costs involved, but it backed by David Lloyd George. Greece’s military defeats made even that proposition untenable by 1922.

The result was the revised Treaty of Lausanne, which with a few minor exceptions (e.g. Hatay province, the disputed Iraqi border) established the borders of modern Turkey.

The most significant update to this has arguably been the Montreaux Convention (1936), which governs Turkish control of the straits and remains in force.