Robbins has been with the network equipment company since 1997. Most recently, he was senior vice president of worldwide operations.
He was a key player in Cisco's strategy for the commercial business segment, which grew 8 percent year over year last quarter, and now represents 25 percent of the company's total business.
Chambers will continue in his role as chairman of Cisco's board of directors.
He has expanded the company from $1.2 billion in annual revenue to its $48 billion, according to Cisco's statement announcing the leadership change. The company also said non-GAAP earnings per share under Chambers' tenure grew more than 3,000 percent.