As satisfying as the swipe to close feature in mobile Safari is, it becomes a bit of a chore to close more than a few tabs.

To close all tabs at once, tap the new tab icon (two overlapping squares), tap Private, and then Close All. Repeat the first two steps and tap ‘+’ (or the screen) to get back to an empty Safari in your preferred browsing state.

I only have an iOS 7 device to test this in.

[crarko adds: I tested this, and it works as described. I also only have iOS 7.]

Source: Mac OSX Hints