Cordero's wife, celebrity fitness instructor Amanda Kloots, announced the good news Tuesday.
Kloots started a hashtag #WakeUpNick that became a movement across social media with fans dancing to Cordero's song "Live Your Life" to show support for the Broadway star.
"Guys, we might have to change our hashtag to #CodeRocky because Nick, Dadda, is awake!" Kloots shared on her Instagram story while holding the couple's son, Elvis.
She said he is officially awake but is still very weak.
Kloots said that even opening and closings his eyes takes all of his energy and he can't close his mouth yet. But he is following commands which she wrote means his mental status is coming back.
"For four weeks we've been waiting for him to wake up, every time I talk to the doctors, they always end it with we just need that mental status, we need to wake him up, we need him to wake up, and it's just been this heaviness that has kind of held over us for this time and to get the news today - the doctors said I think we can officially say he is awake and I mean that was just the best news you could hear," Kloots exclusively told "Good Morning America" later Tuesday night.
Cordero, 41, a Tony-nominated actor, initially went to the hospital March 31 with what they thought was pneumonia, according to Kloots. He later tested positive for COVID-19 and was put in a medically induced coma to help his breathing.
Kloots says blood thinners that were initially helping to ease some clotting in Cordero's leg began causing issues with his blood pressure and he had to have his leg amputated in April.
The illness virtually snuck up on Cordero, the former star of "Bullets Over Broadway," who first just experienced fatigue, Kloots told "Good Morning America."
"We were watching the news and we were trying to decide if this was the coronavirus," Kloots said. "It didn't seem like Nick had the symptoms. He just had this extreme fatigue. We just thought we'd ride it out. We'd see what happened and just isolate because all he wanted to do was sleep."
The couple has a son, 10-month-old Elvis Eduardo.
MORE CORONAVIRUS COVID-19 COVERAGE
UPDATES
Grieving the lost: Tri-State residents who have died
New York state
New Jersey
Connecticut
Long Island
RESOURCES
Where are the testing centers
See how our communities are making a difference
Free educational resources for parents and children
How you can help victims of coronavirus
RELATED INFORMATION
Share your coronavirus story with Eyewitness News
Stimulus check scams and other coronavirus hoaxes
Coronavirus prevention: how clean are your hands?
Centers for Disease Control and Prevention on coronavirus
Total count of NYC COVID-19 cases based on patient address