Well, below is from Wikipedia. And, as we all know, if it is on the internet, it must be 100% true, or the automated accuracy filters would not allow it :-D
"After a few failed attempts at persuading the Icelandic government by diplomatic means to join the Allies and becoming a co-belligerent in the war against the Axis forces, the British invaded Iceland on 10 May 1940. The initial force of 746 British Royal Marines commanded by Colonel Robert Sturges was replaced on 17 May by a larger Army force, and eventually 25,000 British troops were stationed in Iceland.
On 7 July 1941, the defence of Iceland was transferred from Britain to the (still officially neutral) United States, by agreement with Iceland, and US marines replaced the British. Iceland’s strategic position along the North Atlantic sea-lanes, perfect for air and naval bases, could bring new importance to the island. The 1st Marine Brigade consisting of approximately 4,100 troops garrisoned Iceland until early 1942 when they were replaced by U.S. Army troops, so they could join their fellow Marines fighting in the Pacific."