Despite scoring just three goals in the Championship with Wolves, Bodvarsson established himself as a fans' favourite but it soon became apparent that he did not feature in Nuno Espirito Santo's plans at Molineux.
Ipswich Town had been linked with his signature, but both Championship clubs have moved to confirm his switch to the Madejski Stadium for an undisclosed fee.
Manager Jaap Stam told the club's official website: "Jon is the type of player who can play in our system and he is able to play in a number of different positions within that system too - up front as a central striker, as one of a two or as a winger.
"He's a strong runner, he's tall but he's very comfortable on the ball, he's got some pace, so he's definitely a player who will be a useful addition to our squad."
Bodvarsson featured in all but four of Wolves' league games last season, although 20 of his outings came from the bench.