The 25-year-old, who can play in midfield or defence, had been at Villa Park for four years, making 115 appearances for the Villans in the Premier League and Championship.
"Leandro is a player that we have been following for a while – he has played Premier League football and brings quality to us," Stam said. "He is the type of player who can play in several positions in the team – in midfield, at the back, or even sometimes as a winger.
"He is a player with the right mentality and who wants to go forward; these are the types of players that we want to have."
Chief exec Ron Gourlay added: "It gives us great pleasure to secure Leandro's signature and to welcome him to his new home at Madejski Stadium.
"He is a player whose qualities we believe can improve the team and we have worked hard to bring him here, and now that the deal is over the line we are all looking forward to seeing Leandro in the blue and white hoops."
Bacuna, who will wear the number 19 shirt, goes straight into contention for his new side's encounter with Villa on Tuesday night.