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.
It has also said that the rush of sign-ups since the change to WhatsApp’s terms have meant that the app has broken a number of records.
“We continue to shatter traffic records and add capacity as more and more people come to terms with how much they dislike Facebook's new terms," it tweeted. "If you weren't able to create a new group recently, please try again. New servers are ready to serve you.”
At times, Signal has struggled to cope with the influx of interest. It said last week that the verification codes it sends out to users who sign up were experiencing delays, because carriers were struggling to deliver the rush of text messages.
Since then, the company has said that its technology has caught up with the run of users. “Even though we're still breaking records, verification codes are back in the groove,” it tweeted over the weekend.
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