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Bialik, who starred in the 1990s sitcom "Blossom," and Michael Stone have two sons together.
"Divorce is terribly sad, painful and incomprehensible for children," Bialik, 36, said in the statement. "It is not something we have decided lightly."
Bialik, a proponent of "attachment parenting" who authored a book on the subject that was published in September, said it "played no role" in the couple's divorce.
Attachment parenting advocates the nurturing of strong bonds between parents and children, which can include extended breast-feeding and parents and children sleeping in the same bed until the children are as old as 7.
A controversial Time magazine cover on the subject in May drew strong reactions across the United States.
"The main priority for us now is to make the transition to two loving homes as smooth and painless as possible," Bialik wrote in the statement, which was posted to her Facebook page. "Our sons deserve parents committed to their growth and health and that's what we are focusing on."
"We will be OK," the statement concludes.
Bialik is a former child star who appeared in the 1980s television series "Webster" and "The Facts of Life" before landing the title role in the coming-of-age television show "Blossom," which ran from 1991 to 1995. The show was about a smart teenage girl whose parents have divorced and is learning about life.
The actress attended the University of California, Los Angeles, where she obtained a doctorate in neuroscience.
She met Michael Stone, a fellow graduate student, in calculus class, according to a description of her wedding she previously posted online.
In her most recent role on CBS comedy "The Big Bang Theory," Bialik plays Amy Farrah Fowler, a neuroscientist who dates one of the two main stars of the show, the socially inept but brilliant physicist Sheldon Cooper.