Calderoni, who has been serving as interim chief financial officer at the business-to-business software company, replaces Ariba founder Keith Krach, who was the interim CEO and will continue to serve as chairman.
Shares were up 41 cents to $2.91 in afternoon trading.
Calderoni will be Ariba's third chief executive since the beginning of the year. Former president and chief operating officer Larry Mueller was moved to the top spot in April, then left abruptly in July.
Calderoni, who will continue to serve as interim CFO until a replacement is found, was also named to Ariba's board on Wednesday. He previously served as CFO for Avery Dennison, and has worked for Apple Computer and IBM.
Separately, Ariba officials said Wednesday that fourth-quarter revenues are expected to be between $62 million and $63 million, compared to the $59 million analysts were expecting.
Ariba had said in July that it expected fourth-quarter sales to be between $60 million and $70 million, a 25 percent drop from the third quarter.
Ariba also said board member Hatim Tyabji will retire due to health reasons.