General Electric Co. unveiled plans Tuesday to shed two big business units, the culmination of a drastic effort to revitalize what once was one of the U.S.’s largest and most-valuable companies.

Chief Executive John Flannery, whose first year on the job saw a sharp decline in GE’s stock price, said the company would spin off its health-care division and sell its ownership stake in oil-services company Baker Hughes. The two businesses, coupled with its railroad locomotive unit that is being sold, accounted for a third of GE’s...