The DJ died last week from an apparent self-inflicted gunshot wound, it has been reported. He was 40 years old.
Taking to Twitter, Ellen began her video saying: "The last 11 days have been really tough for everyone. Everyone is in pain and trying to make sense of it, and we'll never make sense of it."
"The best thing we can do is to laugh and hug each other and play games and dance and sing... the things he loved to do," she said in the emotional clip.
Ellen explained: "It seems impossible, but that's how we honour him. And hug each other and tell each other we love each other and let people know we're there for them and check in with people."
It comes after tWitch's wife Allison Holker broke her social media silence as she shared a heartfelt tribute after his sudden suicide last week.
Taking to Instagram on Wednesday, 34-year-old Allison posted a picture of herself and Stephen, who rose to fame on the Ellen Show, as she opened up about her grief.
Law enforcement sources said that police discovered Stephen's message at the Los Angeles hotel where his body was found. The note is thought to contain references to issues he had been dealing with.
It is unclear exactly what the Ellen DeGeneres Show star was referring to in his note.
Stephen's wife Allison Holker is said to have run into an LAPD station on Tuesday after she was left deeply concerned he had left home without his car, which was unlike him.
A short time later, the police received a call for a shooting at an LA hotel, where Stephen was found dead, according to TMZ.
The publication says that investigators have determined tWitch took an Uber from his home to the hotel on Monday morning.
He is thought to have turned his phone to airplane mode so no one could reach him.
Allison has been left heartbroken by her husband's death and vowed to honour his memory, saying "his positive impact will continue to be felt".
"He was the backbone of our family, the best husband and father, and an inspiration to his fans. To say he left a legacy would be an understatement," Allison said in a statement to People.
The 34-year-old asked for privacy during this difficult time as she and their three children — Weslie, 14, Maddox, six, and Zaia, three — attempt to move on from this tragedy.
Allison concluded her statement by saying Stephen is missed and that she will "always save the last dance" for him.