Dohmke, currently chief product officer, will replace Nat Friedman from November 15, who will move into the role of Chairman Emeritus.
Dohmke joined GitHub in 2018 after leading the acquisition by Microsoft with Friedman.
"As Chief Product Officer, I'm proud of the work our teams have done to bring new capabilities to GitHub Codespaces, Issues, Copilot, and many of the 20,000 improvements that we shipped last year," Dohmke said in a blog post.
GitHub will retain its developer-first values, distinctive spirit, and open extensibility.
"We will always support developers in their choice of any language, license, tool, platform, or cloud," Dohmke said.
More than 73 million developers are currently building the future of software on GitHub.
In 2020, more than 1.8 million developers in India joined GitHub, taking the developer community in the country to over 5.8 million.
According to Friedman, the company counts 84 per cent of the Fortune 100 as its customers, "and every year since the acquisition, our business has grown more than the last".
Companies such as Infosys, InMobi, Udaan, ShareChat, Capillary Technologies, Swiggy, ArisGlobal and several others have selected GitHub to collaborate and build the software that powers their businesses, accelerating digital transformation.
In June 2018, Microsoft acquired GitHub, a popular code-repository service used by many developers and large companies, for $7.5 billion in stock.
"I am grateful to Satya Nadella and to Scott Guthrie for their support for the GitHub team, belief in the power of our platform, and for their mentorship," said Friedman.
"Development itself is moving to the cloud. AI is revolutionising the way we code. Software security is global security. Open source permeates nearly every product -- digital or physical. Developers are building the future as we type," he added.