"I am truly sorry for the mistakes I have made and for the pain I've caused my family," Dean acknowledged in a statement to People. "I take full responsibility for my actions and have voluntarily checked myself into a treatment centre to address some health and personal issues.
"I am grateful to get the help I need so I can become the husband and father my family deserves."
The 47-year-old is believed to be receiving intense treatment in rehab, but is allowed to leave the facility to visit the couple's four children, Liam, six, Stella, five, Hattie, two and 15-month-old Finn.
Reports about Dean's infidelity emerged over Christmas, but his wife of seven years is yet to address them.
On Christmas Day, Tori posted a picture of her four children posing in front of their beautifully decorated tree, wishing her fans a "Merry Christmas from the McDermotts".
And she sent a strong message at New Year by posting a photograph of the couple cuddled up with Liam and Stella.
"We rang in the New Year with (kid-friendly) cocktails, lots of yummy treats and some quality family time," the 40-year-old wrote on her blog.
Despite her brave exterior, Tori is said to be "devastated" and "much more heartbroken that anyone realised" about the situation.
She is said to be staying strong for her children, but a friend told People, "She could stay with him, or not. God only knows."