ABC News' Felicia Patinkin and Suzan Clarke report:
"I am. I am an alcoholic," Vargas told "GMA" co-anchor George Stephanopoulos in interview that was taped Thursday and aired for the first time today. "It took me a long time to admit that to myself. It took me a long time to admit it to my family, but I am.
"The amount of energy I expended keeping that secret and keeping this problem hidden from view was exhausting," Vargas said, adding that she had done hour-long "20/20" specials on drinking but couldn't acknowledge she had a problem.
"Even to admit it to myself was admitting, I thought, that I was a failure," Vargas, who has anchored on "GMA," said.
"I started thinking 'Well, you know, I'll only drink, you know, on weekends," she said, laughing. "I'll only drink, you know, two glasses of wine a night. I won't drink on nights before I have to get up and do 'Good Morning America.' But those deals never work."
Vargas sought treatment in rehab last fall, and said she's ready to return to the air tonight on "20/20."
'You Can't Tell Anyone What's Happening'
She called her drinking a "staggering burden" to carry.
"You become so isolated with the secret and so lonely, because you can't tell anyone what's happening," she said.
Vargas, 51, said she'd battled panic attacks since she was a child. Her father had left to serve in the Vietnam War, and when her mother would leave home to go to work, Vargas said she suffered daily panic attacks that continued into adulthood.
"I dealt with that anxiety, and with the stress that the anxiety brought by starting to drink. And it slowly escalated and got worse and worse," she said.
Asked whether anyone close to her knew what was happening, Vargas said her husband, musician Marc Cohn, did.
"'You have a problem. You're an alcoholic,'" she recalled her husband saying to her, adding that "it made me really angry, really angry. But he was right."
She said it took her a long time to do anything about it.
"I mean, denial is huge for any alcoholic, especially for a functioning alcoholic, because I, you know, I'm not living under a bridge. I haven't been arrested," she said.
But when she showed up for a "20/20" shoot one day and realized she was "in no shape to do that interview," Vargas said she knew she had to get help.
Vargas, who has two sons, said wine was her go-to drink.
"At night I - that was a ritual," she said. "I should've realized it was a problem way back when Zachary, my oldest son, was born. And he used to call my nightly glass of wine 'mommy's juice.' You know, and I thought that was hysterical. It didn't occur to me that that was a problem."
Vargas said alcoholism was "a progressive, deadly disease," and said she didn't start drinking until later in life.
She described having a panic attack on live television when she was anchoring local news in Chicago. She took beta blockers for her anxiety.
"That's exhausting, to live like that. And it becomes very easy to think 'I deserve this glass of wine. I'm so stressed out … ," she said.
"I felt like I had to be, you know, perfect, which is ridiculous," she said. "Nobody's perfect."
She went to a rehab center that specializes in treating trauma, stayed for 28 days, then left against doctors' advice and came home.
'This Isn't What I Want to Be Known For'
"And they said, 'We think you need to do more work,'" she said. "And I came home for five days and realized they were right, and I went back and finished and stayed until the doctors there said I was ready to come back.
"You know, this isn't what I want to be known for, but I'm really proud of what I did," she said.
When Stephanopoulos asked her how she knew she was ready to come home, she replied: "It's a psychic change, I think. I mean, it's learning to accept that I'm human. That there's nothing wrong with failing, that there's nothing wrong with feeling anxiety."
She said her husband and children were relieved.
She explained to her boys, ages 7 and 10, that she had an allergy to alcohol.
"I didn't want to use the word 'disease' with them, even though that's how it's classified by the medical profession," she said. "It's too scary, you know, the connotation for them is disease is something deadly … and we explained that I was going away to get better. And they came and visited me.
"But I think they're OK," she said. "They're going to be OK."
Vargas admits that it's still hard not to drink but said she feels very strong and has a great support system in place.
"I'm part of AA," she said, referring to the group Alcoholics Anonymous. "I have a sponsor. I have great, great friends who I love and who love me."
She said her triggers were daily stress, then added: "Listen, there are lots of people who feel a lot of stress. Not everybody turns to a glass of wine or three like I did, or four, like I did on some occasions. What I learned to do when I was away was to feel the feelings.
"You know what? They're not going to kill you. You have to experience them. I never learned that skill and (it) makes it tough some days," she said. "Alcohol for me is no longer an option."
Instead of turning to alcohol, she now calls a friend, or meditates or prays.
"There's been a real spiritual component for me in all of this," she said. "Reach out to somebody who can talk you through that rotten day."