One of Hollywood's most eligible bachelors is off the market.  George Clooney and his girlfriend, Amal Alamuddin, are engaged.

A source tells 'People' magazine that Clooney popped the question, but is trying to keep it low-key.  Alamuddin has been seen with a huge diamond on her ring finger.

Clooney is 52 years old and Alamuddin is a 36 year-old British attorney who specializes in international law and human rights.  They've been dating for less than a year.