In his 30 years at International Business Machines Corp., incoming Chief Executive Arvind Krishna has witnessed what works in corporate turnarounds and, more recently, what doesn’t.

Mr. Krishna, 57 years old, is only the 10th chief executive in IBM’s 108-year history. He takes over a company that has been in transition for almost the entirety of his predecessor Ginni Rometty’s eight-year run in the job.

The problems are clear. IBM sales have fallen around 25% in the past eight years, as other tech companies’ top lines have soared. In the hottest field in business technology today, cloud computing—where companies rent rather than buy computing horsepower—IBM trails leaders Amazon.com Inc. and Microsoft Corp. by a wide margin.

Catching such strong rivals “is going to be a challenge,” said David Bahnsen, chief investment officer of the Newport Beach, Calif.-based Bahnsen Group, which has more than $2.25 billion of assets under management and is a holder of IBM stock. He welcomed Mr. Krishna’s appointment, saying he had a good chance of using the company’s strong cash flow to deliver growth in new areas.

Shares of IBM rose 4% in midday trading Friday to $142.42, despite the selloff occurring in the broader market.