Amanda Berry, Gina DeJesus and Michelle Knight appear separately in the three-minute, 30-second video in which they thank the community and talk about moving forward with their lives.
The Plain Dealer in Cleveland reports: "It's obvious the video was shot in an office overlooking the Rock and Roll Hall of Fame and Museum, which is seen outside the window."
Berry says she is "happy to be home with her family and friends." She adds she's getting "stronger each day" and asks that everyone continue to respect her privacy.
The women also express gratitude to the Cleveland Courage Fund, which raised more than $1 million from around the world. Officials say 100 percent of the money will go to DeJesus, Knight, Berry and Berry's daughter, who was born during her captivity.
In the video, DeJesus and her parents thank everyone who donated for their support.
Knight, who is the last to speak on the video, says she is "doing just fine."
She adds: "I may have been through hell and back, but I am strong enough to walk through hell with a smile on my face and with my head held high and with my feet firmly on the ground."
Defiantly, she says, "I will not let the situation define who I am. I will define the situation."
The three women were abducted separately between 2002 and 2004. They managed to break free in May.
Ariel Castro of Cleveland is accused of abducting them and holding them hostage. He has pleaded not guilty to kidnapping, rape and murder charges. Additional charges are expected to be filed.
James Wooley, an attorney for Berry and DeJesus, also issued a statement saying the women do not want to discuss the case with the news media or anyone else.