Sources familiar tell TMZ ... Taryn and Anne Cline broke up in late August. We're told they tried to work it out but ultimately decided they'd be better apart.

A source close to Taryn claims she only said "yes" at the time because Anne put her on the spot ... and after being engaged it just was not the right relationship for her, so she ended it.

Fans had previously speculated they broke up when they stopped following each other on social media in September.

As for Taryn ... we're told she's since moved on from the relationship. In fact ... our sources say she's already seeing someone new. We're told she met a man on set who works in production.

We're told he's the guy in the driver's seat in that☝🏽 Instagram post Taryn posted about a week ago.

TMZ broke the story ... Anne got down on bended knee and asked Taryn to marry her.

The "Orange Is the New Black" actress was shocked when her singer-songwriter GF at the time stopped in the middle of her performance in Florida to pop the question.