Where did the idea of an old Earth come from?

Genesis

Prior to 1750, prominent geologists like Niels Steensen concluded that sedimentary rocks were laid down by Noah’s Flood and that the Earth was roughly 6,000 years old.  Others at that time supported his conclusion.  In the later decades of the 18th century (remember this was during the Age of Enlightenment where people started to doubt the Bible), some French and Italian geologists rejected the global flood and stated that the sedimentary rock layers were created over long periods of time and caused by natural processes.  Other scientists formed views that Earth has experienced catastrophic events during the millions of years in Earth’s past before man was created.

James Hutton (1790s) and Charles Lyell (1820s) were both influential people of their time who wanted to provide evidence to show that slow and gradual processes occurred over long periods of time.  They also wanted to take the science away from the Bible and make it look like it is full of errors.  Charles Lyell published Principles of Geology where he proposed uniformitarianism, thus rejecting continental and global catastrophic floods.  His three volume book was very influential in destroying the ideas of a young Earth, and he even stated that his goal was to take geology away from Moses.  By the end of the 19th century, the age of the Earth was considered by all geologists to be in the hundreds of millions of years.  Over the course of the 20th century, that age increased to 4.5 billion years.

RTG recommends the following book to for more information about the falling away from young-earth views: The Great Turning Point 

This article summarizes the historical change from young-earth to old-earth: http://www.answersingenesis.org/home/area/bios/Scriptural_geologists.asp