Intel shares jumped more than 9.6% to $58.41 after CNBC broke the story ahead of the stock market open. Intel later confirmed the report in a press release.
Swan was named CEO in January 2019. At the time, TheStreet's Jim Cramer said he was surprised by the move due to Swan's previous comments saying he wasn't interested in the position.
Gelsinger, 59 years old, has been in the tech industry for more than 40 years and has served as CEO of VMware since 2012, doubling the size of the company during his tenure.
Gelsinger will also join Intel's board of directors upon assuming the role.
Swan, 60, took over as the permanent CEO after serving as interim CEO. He served as the company's chief financial officer between 2016 and 2019.
Swan replaced former CEO Brian Krzanich, who resigned in June 2018.
VMware shares were falling 5.8% to $134.58 on the news Wednesday.
In December, hedge fund Third Point urged Intel's board to explore strategic alternatives as Intel continued to lose market share to rivals
For the fourth quarter, Intel guided for revenue of $17.4 billion (down 14% annually) and non-GAAP EPS of $1.10. Those numbers, respectively, compared with consensus estimates of $17.38 billion and $1.07.
Intel is scheduled to report its fourth-quarter results at the end of January.
In October, the company reported third-quarter revenue of $18.33 billion (down 4% annually) and non-GAAP earnings of $1.11 a share. Revenue slightly topped an $18.24 billion FactSet consensus, while EPS was in-line with consensus.