I got my final divorce decree in the US from my first marriage 7 months ago, does the 300 days period after divorce apply to me as a foreigner before I marry a Turkish man, or is it mandatory only for Turkish women?

If I marry my Turkish fiance in the USA, is the marriage automatically legal in Turkey, or do we have to register it in Turkey in order for it to follow the Turkish laws, or do we have to get married again in Turkey?