The milestone was reached earlier this month, the EFF said in a statement.
It quoted figures from Mozilla that showed the volume of encrypted traffic on Firefox exceeded the quantum of unencrypted traffic.
Google's figures for its Chrome browser showed a similar spread, showing that more than half the pages loaded across different operating systems were protected by HTTPS.
The organisation said it had been pushing for encryption across the Web since 2010. Facebook and Twitter implemented HTTPS by default and this was followed by Wikipedia and other highly-trafficked sites.
The EFF had joined with the Tor Project, which produces the Tor browser, to create HTTPS Everywhere, a browser extension that forces the use of encrypted pages wherever possible.
The EFF also said it had helped found a certificate authority known as Let's Encrypt along with Mozilla and the University of Michigan, with Cisco and Akamai being sponsors. Using the Certbot tool, webmasters could obtain a free certificate from Let's Encrypt and automatically configure their servers to use it.