Bacuna, 25, played 131 times in four years with Villa and started their opening Championship game of the season against Hull on 5 August.
The Curacao international could make his Royals debut against Villa when the sides meet each other on Tuesday.
"He has played Premier League football and brings quality to us," said Reading manager Jaap Stam.
Find all the latest football transfers on our dedicated page.
Reading have signed midfielder Leandro Bacuna from Aston Villa on a four-year contract.