The 23-year-old can play at left-back or in the centre of defence and is set to make his Rovers debut in Saturday's Championship game against QPR.
Republic of Ireland U21 international Stevens joined Villa from Shamrock Rovers in January 2012 and made his first-team debut in the 3-0 Capital One Cup victory over Tranmere on August 28 last year.
He then played against Swindon in the same competition before making seven Premier League appearances, including six starts.
However he has not featured for Villa since the 1-0 home defeat to Southampton on January 12.
Stevens was loaned out to Notts County earlier this season and made four appearances for the League One club.