Topsy is one of the few firms to have access to Twitter’s entire data stream.
It has recently created a searchable database of all tweets sent – more than 400 billion – since Twitter’s launch.
Apple did not say how much it paid for the firm, but the Wall Street Journal which first reported the story put the figure at around $200m (£122m).
Topsy competes with firms like DataSift and Gnip to figure out who is influential on Twitter, what terms are trending, and the impact of specific Twitter campaigns.
It is Apple’s second acquisition in recent weeks.
Last month, it announced it had bought Israeli firm PrimeSense, which specialises in making 3-D motion detection technology.
Apple is one of the world’s biggest firms in the technology sector but the firm is not known for its forays into the world of social media.
The company’s earlier effort at social networking – the Ping music sharing service – failed to catch on with consumers.
As it confirmed the latest deal, an Apple spokesperson declined to give details of the firm’s plans with Topsy.
“Apple buys smaller technology companies from time to time and we generally do not discuss our purpose,” the spokesperson said.
However, some analysts said Apple could look to use the data analytics for a variety of purposes, not least a better placement of its products across social media.
“There are millions of people sharing their thoughts on platforms such as Twitter on any given day,” Sanjana Chappalli, Asia-Pac head of LEWIS Pulse, a firm specialising in digital marketing services, told the BBC.
“For companies to be able to understand what is popular with these users and what they are interested in, and then use it to their advantage, they need to filter the content and understand it.
“Topsy gives Apple the tools to do just that,” she explained.
Manoj Menon, managing director as consulting firm Frost & Sullivan added: “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, companies operating internet search engines have also been looking to tap into the social media sector to try and offer more personalised search results to users.
“They are looking at what your friends are commenting on or tweeting about and then giving you similar recommendations when you look for information online,” said Ms Chappalli.
She added that search engines such as Google and Bing have been moving in that direction for some time.
“Apple, with its Safari web browser on all its devices, could do with such an analytics capability provided by Topsy to achieve that,” she added.
At the same time, some analysts suggested that Apple could also use Topsy’s 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.