Intel's stock was rose nearly 7% on Wednesday. VMWare's stock fell nearly 7%.
Swan was named CEO in January 2019 after serving as interim CEO for seven months.
During Swan's tenure, Intel has suffered blows from competitors. Over the summer, Intel reported that its latest generation chips would be delayed while AMD's were already shipping inside laptops. Apple announced in the fall that it will use its own proprietary chips in its Mac computers, breaking a 15-year partnership with Intel for its chip supplies.
Dan Loeb's Third Point hedge fund in December urged Intel's board to explore "strategic alternatives." That came after Intel lost market share to competitors AMD, Samsung and TSMC.
Third Point urged Intel to divest from "failed acquisitions" and criticized Intel for its "loss of manufacturing leadership." The firm recently took a roughly $1 billion stake in Intel, according to Reuters.
Following the news of Swan's departure, Loeb called him "a class act" and said he "did the right thing for all stake holders stepping aside for Gelsinger."
Critics have pointed to the fact that Intel's chief executive did not come from a technical background, having previously served as CFO. With Gelsinger, that will no longer be the case. Gelsinger previously worked at Intel, eventually becoming its first chief technology officer.
Intel said the announcement was separate from its financial results and said it expects fourth quarter 2020 revenue and earnings to exceed prior guidance. The company said it "has made strong progress" on its latest generation 7 nanometer chips, which it said it would discuss when it reports earnings on Jan. 21.