The number on all nine accounts put together went over five million for the first time on Thursday.
The comments on the tweets left by followers are often irreverent and chatty, with one user asking the pope on Thursday: "How you settling in?"
Benedict launched the account on December 12 after encouraging Catholic Church leaders to use social media to reach a wider and more youthful audience.
The Vatican has said the tweets are approved by the pope although not actually written by him and are sent from a single computer to avoid hacking.
Francis' latest tweet on Thursday reads: "God loves us. We must not be afraid to love him." His first tweet a few days after his election read: "I thank you from my heart and I ask you to continue to pray for me."
The pope has shown a tradition-breaking style in his first few weeks in office and has said he wants the Church to be closer to ordinary people.
The number of followers on the Spanish-language account of Latin America's first pope has risen particularly sharply to 1.6 million, although the Argentinian was still trailing in Portuguese with 188,000 followers.