As on August 25, Modi had over 22.1 million followers on the social networking platform, while Bachchan marginally trailed with 22 million at last count.
In January, Modi's Twitter followers surpassed that of Bollywood superstar Shah Rukh Khan. Modi, then, became the second most followed Indian on Twitter with over 17,371,600 followers, compared to Khan's 17,351,100.
Now, Khan is the third most followed Indian on Twitter with 20.9 million users of the social media site following him.
The number of followers of Modi's account (@narendramodi) consistently increased by about a million every two months in 2015.
It crossed the 15 million mark on September 22 last year, and touched 16 million on November 20.
In 2016, the growth rate of Modi's Twitter followers slowed down, with about 5 million users being added in around eight months.
Active on Twitter since 2009, Modi is also the second most followed politician in the world, right after US President Barack Obama (@barackobama), as per Twitter.
Modi has used Twitter for campaigns like #MakeInIndia, #SwachBharat, #MannKiBaat and #SelfieWithDaughter to reach and connect with citizens.
Government is encouraging people and officials to use Twitter to communicate with each other.
(With inputs from PTI)