It now shows as the top free app on both the Google Play Store and Apple’s App Store, in a variety of countries.
Signal, which encrypts conversations and is run by the non-profit Signal Foundation, has become a key competitor to WhatsApp as users look to keep their information secure.
It received yet more attention in recent days amid concern over a new update to WhatsApp’s terms that led to suggestions the app could be sharing private data with Facebook.
WhatsApp has denied there will be any significant change to its data policies, but many including Elon Musk and Edward Snowden have urged users to switch anyway.
Mr Musk’s tweet has since been shared 52,000 times, and likely helped propel the app to its current popularity.
Signal has criticised Facebook, including the fact that it has bought ads in the iOS App Store so that users searching for the name of the app will be shown the link to download its own Messenger instead.