On the morning of January 17, 1917, Room 40 intercepted a coded German diplomatic message from Foreign Secretary Zimmermann to Count von Bernstorff, the German ambassador in Washington.
Room 40 was able to do so in two ways.  Because neutral but pro-German Sweden was transmitting messages for Germany, the British had tapped into the Swedish cable to South America where it passed by England.  Zimmermann had sent one copy of his telegram by this route, with instruction that the German ambassador in Buenos Aires forward it to Washington.  Room 40 got it!

To ensure receipt, however, Zimmermann had sent it in a second and for more audacious way: he had the American ambassador in Berlin telegraph it to the State Department in Washington, which in turn hand-delivered it to the German embassy.  This arrangement had been made possible by President Wilson, who was trying to mediate an end to the war and had offered to transmit German diplomatic message to Washington when the Germans protested that they had no capability to communicate confidentially with their ambassador there.  This copy traveled via Copenhagen, then London, on its way to the United States, with instructions to the German ambassador to forward it to Mexico.  Room 40 got it when it passed through London.

Both versions of Zimmermann’s telegram were enciphered using code 0075, which the British had already partially broken.  With two copies at their disposal, they were able to piece together enough of the message recognize substance of it.  Admiral William Hall, Director of Naval Intelligence and head of Room 40, ordered that the existence of the telegram be kept secret from all other agencies while Room 40 cryptographers filled in the gaps in the message. The British used intercept of other German traffic sent in code 0075 to recover additional codegroups, and by February 5 the task was sufficiently complete for Hall to share it with the British Foreign Office.

Source: NSA.gov