The 50-year-old attracted almost five million followers in 12 hours after posting a selfie with Lisa Kudrow, Courteney Cox, Matt LeBlanc, David Schwimmer and Matthew Perry.
The post followed her recent revelation that the cast had met up at Cox's home.
"And now we're Instagram FRIENDS too. HI INSTAGRAM," the actress wrote.
After her profile appeared not to accept new followers for a short time because of a technical difficulty, Aniston joked: "Sorry, I think I broke it."
Her post has been liked by more than eight million users, while her current follower count stands at 7.3 million.
The actress reportedly gained more than 116,000 followers within 30 minutes of creating her account.
It's likely she now holds the record for having the fastest Instagram account to reach one million followers.
According to Guinness World Records, Prince Harry and his wife Meghan have held that title since April when their joint account reached that milestone in five hours and 45 minutes.
It is believed Aniston's account surpassed that record in a far shorter period, though this has yet to be officially verified.
Mariah Carey, Kate Hudson and Reese Witherspoon are among a number of celebrities who have posted messages welcoming Aniston to the platform.
"YASSSS!!! Welcome to Insta Jen!!!" wrote Witherspoon, who appears with the actress in her new Apple TV series The Morning Show.