“It is an extraordinarily sad moment, but I love my children more than anything and still care deeply about Elizabeth," the former two-time Democratic presidential candidate says in a statement.
In a cover story on newsstands Friday, PEOPLE reports that last December, in a mediated visit in a North Carolina hotel, Elizabeth met the 23-month-old baby whom John had fathered with a mistress.
After that, "She said, 'I've had it. I can't do this. I want my life back,' " Elizabeth's sister, Nancy Anania, tells PEOPLE. The couple now occupy separate residences.
A spokeswoman for Elizabeth has released a statement saying she's "moving on with her life" after a "excruciatingly painful period for her."