Formerly president and chief operating officer, Mueller was tipped to head the B2B prodigy's comeback following disappointing first-quarter earnings, redundancies and the failed US$2.55bn (£1.79bn) acquisition of Agile Software, which the company has blamed on a choppy US economy.
Mueller replaces Keith Krach as CEO. Krach will continue as company chairman.
Mueller, 48, joined Ariba in October 1999 after stints as president and CEO of 3D-modeling company Imageware, executive vice-president for financial software company JD Edwards, and a decade of management positions at IBM.
At Ariba, Mueller has been responsible for championing client cost-savings while growing the business, the company said in a statement.
Mueller has also been awarded a place on the company's board of directors, along with Softbank president and CEO Masayoshi Son, who replaces board member John Mumford, founder of Crosspoint. According to Ariba, Mumford left to concentrate on his entrepreneurial endeavors.
Mueller's promotion is one of a number of staff changes the company has undergone recently in an effort to strengthen its position in the volatile technology market.
Following the announcement of Mueller's promotion, the company's stock (ARBA) was up 4.87% to $7.75 in mid-morning trading on 30 April.