Naomi Watts & Liev Schreiber Broke Up

Naomi Watts and Liev Schreiber have ended their 11-year relationship ... TMZ has confirmed.

They released a joint statement saying, "Over the past few months we've come to the conclusion that the best way forward for us as a family is to separate as a couple."

TMZ learned they were on shaky ground as early as January, when they first discussed splitting, and were already living apart.

They say they'll still be raising their sons -- 9-year-old Alexander and 7-year-old Samuel -- together during "this new phase" of their relationship.

Liev and Naomi were not married, but had been together since 2005 ... shortly before their first film together, "The Painted Veil," was released.