Strangely enough, this option has been around on the iOS counterpart of YouTube for some time now. It was high time to implement it to the Android version of YouTube, Google!
This update will bring your YouTube app to version 5.7 and will enable you to stream at 144p, 240p, 360p, 720p, and 1080p. Additionally, there is an "Auto" option, which chooses the best possible quality based on your current Internet connection. The streaming quality of the video playback can be adjusted from the Settings menu, which is in the upper right corner of the video you are watching.
As usual, the update will be rolling out in stages, so it may not hit your YouTube app right away. Oh, and by the way, we are still waiting for that nifty offline video playback that was promised back in November.
Download: YouTube (Android | iOS)
YouTube quality settings for video streaming
source: Android Central