EXCLUSIVE

Fergie's had enough of the separated life ... she and Josh Duhamel are finally getting divorced ... TMZ has learned.

Fergie filed divorce docs Friday in Pasadena, and no one could call it a rash move. The exes have been apart publicly since September 2017 ... when they announced they were breaking up. In a joint statement, they said they'd actually been separated since earlier in 2017.

However, neither made a move divorce-wise ... until now.

The singer and actor have one child together ... their son Axl, who is 5 years old now.

They'd been married for 8 years before announcing their break-up -- and they had started dating in 2004.

Josh has been dating pretty openly. In the last year, he's been seen out with Rebekah Graf, Eiza Gonzalez ... and just this week he was at Nobu in Malibu with a mystery brunette.

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