However, Wall Street also sees Immelt's move as a chance for redemption, after his departure from GE in the latter half of 2017 capped a rocky 16-year run at the helm that saw the stock lose about 38 percent of its value.
George Hill, an analyst at RBC Capital Markets, believes Immelt could be a "door opener and sales closer" for Massachusetts-based Athenahealth. Immelt can also serve "as a mentor and teacher to Athenahealth's young management team," Hill told clients in a note. "In return, Immelt gets a chance to rehabilitate his image with the investment community."
Athenahealth announced Immelt as its new chairman late Wednesday, and shares of the health-care cloud-based software company were down about 3 percent Thursday. In the past 12 months, Athenahealth shares were up about 15 percent, pretty much matching the performance of the S&P 500.
Immelt is no stranger to activist investors, having dealt with billionaire Trian Partners boss Nelson Peltz, who was a major GE shareholder. He arrives at Athenahealth as Elliott Management pushes for operational and strategic changes to maximize shareholder value.
Immelt succeeds as chairman Athenahealth's colorful co-founder, Jonathan Bush, who remains CEO, a role he's held since the company was founded in 1997.
Don Hooker, an equity research analyst at KeyBanc Capital Markets, described the 48-year-old Bush as a strong entrepreneur and visionary. "Bush will still very much be running things at Athena," Hooker told CNBC. "Investors still want to see that."
But as a visionary, Bush was less inclined to financial discipline, said Hooker, who predicted Immelt will use his decades of experience on Wall Street to develop Athenahealth's businesses and to create new relationships.
"Feedback that I've gotten from inside Athena is that Immelt brings star power," Hooker said. "He's not necessarily a complete expert in health care. But there are a lot of positives." The company cited Immelt's "digital expertise" among the reasons for the appointment.