The guitarist had been in Dylan's live band since 2019, but he bid farewell to his bandmates over the weekend.
Joel Paterson is reportedly Dylan's only guitarist and performed his first concert in Austin, Texas this week.
Britt initially shared an image of a flight on Facebook and captioned it: "Sayanora Bobby."
When asked to clarify his exit, he wrote: "I quit."
The vague post later disappeared, leaving fans to speculate that he had been let go by Dylan.
However, Britt shared an update and explained he left "of his own accord" but would not be disclosing his reason for leaving.
"Apparently there are quite a few threads out there with people speculating about my departure from the Bob tour. I'd like to clear it up. I was not fired but left of my own accord for reasons I would prefer to keep private," Britt posted.
"I will miss my band mates and crew. I am looking forward to getting back to doing sessions (give me a call) and also finishing up Etta's gospel record.
"As far as any touring goes, we will see what the future holds."
It's the latest departure for Dylan in a matter of weeks, after guitarist Doug Lancio was replaced by Julian Lage.
Dylan's North American tour is due to wrap up in August in Nashville.
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