Workers took it off the company's San Francisco headquarters Monday in preparation for Elon Musk's renaming of the platform.
Martin Grasser, one of the three designers behind the blue bird logo, told Reuters he was sad to see it go.
"It represents the best of the internet's adolescence. I think that it recalls a time when we, a lot of people - I don't mean this to sound cynical - but believed more in the power of the Internet."
The rebranding is part of Elon Musk's longer-term goal of shifting it toward an "everything app" in three to five years.
Musk has said he envisions an app that could give users services beyond social media... like peer-to-peer payments.
The idea mirrors WeChat, a wildly popular app in China whose Pay services can be used almost anywhere in that country.
"#GoodbyeTwitter" was trending on Twitter on Monday with reference to the old logo, as well as criticism from users about the new one.
Marketing and branding experts say the rebrand risks throwing away years of Twitter's name recognition.
"I think losing the iconic Twitter logo and the birdie, users are not going to love that."
Wedbush Securities Managing Director Daniel Ives told Reuters the move was "risky".
"When you lose an iconic logo like that, re-brands are dangerous, and, you know, clearly back against the wall for Twitter, and you're seeing that rebrand from start to finish, but I think, kneejerk, this probably detracts from the value that you lose the iconic Twitter birdie."
In a recent investor presentation, Twitter revealed a business revamp to focus more on video and commerce, led by its new Chief Executive Linda Yaccarino, who formerly worked at NBCUniversal.
After Musk acquired Twitter in October, the social media giant faced months of chaos.
It laid off thousands of staff, faced criticism over lax content moderation, and an exodus of advertisers who did not want their ads appearing next to inappropriate content.