Dwight D. Eisenhower was the Supreme Allied Commander during World War 2. Although the Americans joined the war over two years after the start, an American was still made to be the Supreme Commander. Eisenhower was responsible for the planning of D-Day, also known as the Battle of Normandy.
There were multiple Supreme Allied Commander positions though, the others being:
• Supreme Allied Commander of the Allied Expeditionary Forces - Dwight D. Eisenhower
• Supreme Allied Commander Mediterranean - Henry Maitland Wilson and then Harold Alexander
• Supreme Allied Commander South East Asia - Louis Mountbatten
• Supreme Allied Commander South West Pacific Area