Bring water and quinoa to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until quinoa is tender and water has been absorbed, 15 to 20 minutes. Transfer quinoa to a large serving bowl and let cool completely.
Drizzle olive oil over cooled quinoa and stir. Fold olives, feta cheese, tomatoes, and basil through the quinoa.