Cisco said it would pay $55 per share, in cash. BroadSoft shares had closed at $54.90 on Friday, giving the company a market capitalization of $1.67 billion. Shares opened about 1.5 percent higher on Monday after the deal was announced.
The deal, which comes after Reuters first reported in August that BroadSoft was exploring a sale, allows Cisco to further diversify away from its stagnating switches and routers business by giving it a stronger foothold in selling unified communications software to big telecommunications firms.
Cisco CEO told CNBC that the deal will help Cisco's enterprise clients and small businesses connect better with consumers.
"Every customer, when they think about their digital strategies, they think about how they interact with their customers," Robbins told "." "This acquisition of BroadSoft actually gives us the most comprehensive set of collaboration solutions for our customers."
The BroadSoft deal would be Cisco's second major acquisition this year following the $3.7 billion acquisition of privately held AppDynamics in March.
After the 2016 election, Robbins told CNBC that , particularly the repatriation of overseas cash, would prompt Cisco to look into . Cisco's latest deal comes as there is to pass a budget and focus on tax cuts.
When asked on Monday, Robbins told CNBC that the prospect of tax reform did not impact the timing of the BroadSoft deal.
"To date, we have not had any deals that we have considered that we have delayed, or put on hold, because of waiting on repatriation," Robbins said. "Obviously we remain very optimistic about tax reform, and are hopeful that something will happen late this year or early in 2018."
With its traditional business of making switches and routers seeing revenue declines, Cisco, like other legacy technology firms, has been focusing on high-growth areas such as security, the Internet of Things and cloud computing.
Based in Gaithersburg, Maryland, BroadSoft provides software and services that enable mobile, fixed-line and cable service providers to offer unified communications over their internet protocol networks.
BroadSoft has recently tried to revamp its business model to sell directly to these customers, a move that risks its relationships with its telecommunications partners, according to a Barclays Plc research report.
New York-based hedge fund P2 Capital Partners owned a 4.6 percent stake in BroadSoft as of the end of June, according to Thomson Reuters data. P2 has often behaved as an activist shareholder and has even offered to buy companies in which it has invested.
Another BroadSoft shareholder with a history of acquisitions is buyout firm KKR, which is BroadSofts 13th-largest shareholder, according to Thomson Reuters data.
— Reporting by Reuters. CNBC's and the Associated Press contributed to this report.