The reports were confirmed by Tehran-based fashion photographer Reihane Taravati, who along with her friends was arrested for what Tehran police chief Hossen Sajedinia called a "vulgar clip which hurt public chastity."
"Hi I'm back," Taravati said in a post on the Instagram website.
She was allegedly shown on state television last night repenting for the homemade video that was posted on YouTube last month and shared widely on Facebook and Instagram.
The clip has since gone viral, and been viewed more than 265,000 times.
Taravati also thanked Williams for showing support during her brief detention.
The singer had protested over the treatment of the young Iranians on Twitter, saying: "It's beyond sad these kids were arrested for trying to spread happiness" -- referring to the idea behind his original video of dancing in the streets and be happy.
The Iranian authorities are yet to confirm the dancers' release on bail.
The reports of their release came amid an apparent message of support for the group by Iran's President Hassan Rouhani, who is China on an official visit.
"Happiness is our people's right. We shouldn't be too hard on behaviours caused by joy," a Twitter account believed to be run by his close aides, @HassanRouhani, quoted the president from a speech in June 2013 shortly after his election.
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