The former Leeds winger was the Millers' first signing of the close season, but failed to make an impression and after just 10 appearances he was sent to Oakwell on loan in November.
He briefly returned to the club this week at the end of that loan spell but has negotiated an early release from his contract, putting pen to paper with the Reds on a deal until the end of the season.
"The 24-year-old has made 10 appearances in total for the Millers, featuring as a substitute on six different occasions during his stay at AESSEAL New York Stadium.
"White recently impressed on a loan spell at local neighbours Barnsley and made seven appearances for the Tykes after making the switch in late November.
"We would like to thank Aidy for his efforts whilst with the club and wish him all the best in his future endeavours."