Google, with a market value over $130 billion, will pay for YouTube with a block of its own stock (worth $1.65 billion).
The deal combines two of the Internet's most popular brands, used by millions of people a day.
Analysts say the acquisition allows Google, the most-used Internet search engine, to tap into the growing online video industry.
YouTube, founded less than two years ago, allows users to display and share short video films. It began with home videos, but has evolved into a site where users watch up to 100 million short films every day.
Much of the site's current content displays copies or excerpts of popular television shows or films, along with scenes of real events, such as video diaries filmed by soldiers in Iraq.
Many of the film clips posted by YouTube users involve copyrighted material, and many legal experts foresee extensive legal challenges to such free display in the future. Currently, YouTube avoids litigation by removing copies of commercial videos when a copyright holder complains.