Topsy specialises in using data from Twitter to track customer sentiment, and is one of the few firms to have full access to Twitter's stream of tweets.
The Wall Street Journal first reported the news, and said an Apple spokeswoman confirmed the deal to the newspaper but refused any further comment.
Topsy is a tool used by businesses and the general public that can determine how often a specific term is tweeted or retweeted and how the term is used, identify an influential person on a specific subject, or measure the exposure of an advertising event or campaign.
The company's archive contains 425 billion tweets, beginning in 2006 when Twitter first started up until the present day.
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Some analysts have said Apple could look to use the data analytics for a variety of purposes, including a better placement of its products across social media.
"Social media accounts for a significant amount time spent on mobile devices," Manoj Menon, managing director as consulting firm Frost & Sullivan told UK broadcaster BBC.
"Brands across the world are looking at ways to use the time spent by customers on social media to enhance their brands, and Apple is no different."
At the same time, Apple could also use Topsy's analytic technology to its own data, such as information from the App Store.
"Apple may also be able to provide better user experience to customers by integration of analytical capability to its products and services," said Mr Menon.
It is Apple's second acquisition in a week.
As we previously reported the world's most valuable company announced it had bought Israeli firm PrimeSense, which specialises in making 3-D motion detection technology.