Anthropic, best known for its Claude chatbot, had released a series of commercials aimed at OpenAI, criticising the company's move to include adverts for some users.
The company, which was formed in 2021 by a breakaway team of early OpenAI employees, has positioned itself as having a more safety-orientated approach to AI research compared with its rivals.
Sharma led a team there which researched AI safeguards.
He said in his resignation letter, external his contributions included investigating why generative AI systems suck up to users, combatting AI-assisted bioterrorism risks and researching "how AI assistants could make us less human".
But he said despite enjoying his time at the company, it was clear "the time has come to move on".
"The world is in peril. And not just from AI, or bioweapons, but from a whole series of interconnected crises unfolding in this very moment," Sharma wrote.
He said he had "repeatedly seen how hard it is to truly let our values govern our actions" - including at Anthropic which he said "constantly face pressures to set aside what matters most".
Sharma said he would instead look to pursue a poetry degree and writing.
He added in a reply: "I'll be moving back to the UK and letting myself become invisible for a period of time."
Those departing AI firms which have loomed large in the latest generative AI boom - and sought to retain talent with huge salaries or compensation offers - often do so with plenty of shares and benefits intact.
A former OpenAI researcher who resigned this week, in part due to fears of the use of advertising on ChatGPT, has told BBC Newsnight she feels "really nervous about working in the industry".
Zoe Hitzig said her concerns stemmed from the possible psychosocial impacts of a "new type of social interaction" that were not yet understood.
She noted "early warning signs" that dependence on AI tools were "worrisome" and could "reinforce certain kinds of delusions" as well as negatively impacting users' mental health in other ways.
"Creating an economic engine that profits from encouraging these kinds of new relationships before we understand them is really dangerous," she continued.
"We saw what happened with social media" she said, noting "there's still time to set up the social institutions, the forms of regulation that can actually govern this". It was, she said, a "critical moment".
Responding to BBC News, a spokesperson for OpenAI pointed to the firm's principles which state: "Our mission is to ensure AGI benefits all of humanity; our pursuit of advertising is always in support of that mission and making AI more accessible."
They add: "We keep your conversations with ChatGPT private from advertisers, and we never sell your data to advertisers."