The 24-year-old is out of contract at the League One club and will officially join the Whites on a two-year deal on July 1.
Smith becomes Brian McDermott's first signing since the former Reading manager replaced Neil Warnock in April.
Birmingham-born Smith, who began his career at Cheltenham, played non-league football for Solihull Moors before joining Oldham in 2011.
He scored twice in the Latics' FA Cup win over Liverpool last season and headed a stoppage-time equaliser in the following round against Everton before Oldham lost the replay.