The 29-year-old will join the Iron on a free transfer on July 1 and has signed a two-year deal with the club, with the option of a further 12 months.
Dawson was with fellow League One side Rochdale last season, where he made 36 appearances.
The former Republic of Ireland Under-21 international began his career with Leicester City before moving on to Mansfield Town where he made over 120 appearances for the Stags in three years.
He later had a two-year spell at Bury where he made nearly a century of appearances but left the Shakers to join Leyton Orient in 2010 where he scored four goals in 75 games in an 18 month spell at Brisbane Road.
Dawson moved to Barnsley for an undisclosed fee in January 2012 and made 85 outings for the Reds, scoring six times, in two-and-a-half seasons at Oakwell.
He turned down the chance to stay with the South Yorkshire club and joined Rochdale instead, reuniting him with Keith Hill who had signed the midfielder whilst in charge of Barnsley.