The studio is reported to have paid more than $30m (Â£19m) for the title, according to the Hollywood Reporter.
Michael Fassbender is to play Jobs in the film, based on Walter Isaacson's biography of the late entrepreneur.
The real-life drama will be directed by Danny Boyle, from a script by fellow Oscar-winner Aaron Sorkin.
Sony had bought the rights to produce a film based on Isaacson's biography following Jobs' death in 2011.
The studio has not explained why it pulled out, though it had reportedly struggled to fit the film into its schedule.
Director David Fincher was initially set to direct but pulled out of talks in April.
A number of big-name actors have also been attached to the film, among them Leonardo DiCaprio and Christian Bale.
Jobs was a charismatic figure and a master at presenting Apple's latest products. But his career took dramatic turns.
After founding Apple with Steve Wozniak in the late 1970s, he was driven out of the firm in a boardroom coup in the 1980s.
A decade later he was bought back when Apple ran into trouble and presided over an era when it became the most valuable US company and producer of the highly successful iPhone.
He died in October 2011 at the age of 56 after a long battle with pancreatic cancer.
Universal Pictures are to make a film based on the life of Apple co-founder Steve Jobs, following Sony Pictures' departure from the project last week.