The service is regarded as one of the most secure and trustworthy services available for people who are concerned that their communications might be intercepted and has been endorsed by privacy advocates such as Edward Snowden.
The underlying protocol has since been adopted by other messengers includingWhatsApp and is seen as one of the most effective security innovations this century.
Marlinspike - who was born as Matthew Rosenfeld - wrote: "Signal has grown in adoption and popularity around the world even faster than I imagined. People increasingly find value and peace of mind in Signal (technology built for them instead of for their data), and are increasingly willing to sustain it."
Signal describes itself as a "different kind of tech organisation" that doesn't feature "investors, quarterly earnings calls or share price considerations" and asks for donations from users of its free app.
Marlinspike said it was a "good time" for the firm to appoint a new chief executive and says that WhatsApp co-founder Brian Acton has volunteered to replace him on a temporary basis.
Acton sold WhatsApp to Facebook (now known as Meta) in 2014 for £16 billion but exited the company four years later due to a disagreement regarding user privacy.
Marlinspike's resignation follows criticism of his plans to introduce a cryptocurrency transactions feature on Signal, but this was not referenced in the announcement that he would be stepping down.