The 100th Prime Minister of Japan and Leader of the LDP has been decided.
「第100代自由民主党総裁兼内閣総理大臣が決まった」は英語で「The 100th Prime Minister of Japan and Leader of the LDP has been decided.」と言います。LDPより省略なしの「Liberal Democratic Party」を使っても問題ないと思います。
第100代自由民主党総裁兼内閣総理大臣が決まって岸田文雄という人だそうです。
The 100th Prime Minister of Japan and Leader of the LDP has been decided, and I heard it's someone named Fumio Kishida.
The 100th President of the Liberal Democratic Party and Prime Minister has been decided.
「第100代自由民主党総裁兼内閣総理大臣が決まった」の英語表現は「The 100th President of the Liberal Democratic Party and Prime Minister has been decided」となります。ここで「President of the Liberal Democratic Party」は「自由民主党総裁」。「Prime Minister」は「内閣総理大臣」を意味します。