It's a bit complicated. Some say the Uyghurs arrived in that area 900 or so years ago, some say they have been there for over 6400 years. Most likely, modern Uyghurs are descended from a mix of peoples, including the original ancient Uyghurs, the Tiele people, and some other peoples.

China controlled the region about 2000 years ago during the Han Dynasty, but has since lost it and regained control several times throughout history.

The region is historically important as it is on the Silk Road, and has seen a huge amount of wars. So it is likely that the populations there have been displaced several times.

Apparently, modern Uyghurs are part of China because a plane crash killed many of the delegation of the Second East Turkestan Republic who were opposed to being part of China, leaving a surviving leader who joined the Chinese Communist Party.

terrifying!

Here’s the history of it, straight from the horse’s mouth:

https://www.youtube.com/watch?v=xKBTT827b84

If you want to understand Xinjiang, you have to first understand the First Island Chain (and China's recent development in MRBM).