When and how did Great Britain and the United States become such strong allies?

Culturally similar, tensions existed between the US and the UK from the Revolution through the end of the Civil War. WWI and WWII were the building blocks of the trans-atlantic alliance.

The US and UK are allies through mutual national interests. The UK needs US military support to pursue its interests and the US needs British bases throughout the world to project its power. Many key US bases are actually on British territory. Also, if the US wants to project its power somewhere, its politically useful to have even a token British presence on the gunline and at the UN Security Council. Also, since its usually illegal for either country to spy on its own citizens, its handy having a friendly and trustworthy power to do it for you and vice versa.