The original mechanical computer, which used more than 8,000 bronze, iron and steel parts, was never completed by Babbage owing to a lack of funding.
The replica was funded by former Microsoft chief technical officer Nathan Myhrvold, who has put an estimated US$2 million into the project.
"It is the intellectual origin of the industry I have been in and the way I have made all my money," Myhrvold told the BBC.
"Silicon Valley is a society that drives without rear view mirrors. There is an obsession with moving forward and moving fast. There is a feeling that there is no point in looking backwards. I think that is wrong."
The replica was built by Doron Swade, a former curator of computing at the Science Museum in London.
Swade constructed the first Difference Engine No. 2 replica in 1991 to celebrate 200 years since Babbage's birth, and has now completed the second device.
"You can stand in front of this monster of a machine as a Victorian would have done and still have a sense of wonder," he said.
"It takes you back 150 years to a branching point in history and allows you to speculate what might have been had this engine been finished.
"There would not have been the '100 dark years' between Babbage's death and the beginning of the electronic era in the 1930s when pioneers reinvented all the essential principles of computing largely in ignorance of Babbage's designs. "
Myhrvold caused some controversy after leaving Microsoft when he and former Microsoft and Intel employees joined with a Seattle law firm to form Intellectual Ventures, which buys and licenses patents.
US gets own Difference Engine No. 2
By Iain Thomson on May 13, 2008 11:45AM