Financial terms were not disclosed, but multiple outlets, including the Orange County Register, report the deal is worth $600,000.
The pact is contingent on Moreau passing a team physical on Monday.
The 35-year-old was limited to 37 games with Columbus a season ago due to a broken right hand suffered in October and a rib injury in early January. He managed just one goal and six points.
Since breaking into the NHL with Chicago in 1996, the 'Hawks former 1994 first-round pick has compiled 146 goals and 283 points with 1,090 penalty minutes in 900 contests with Chicago, Edmonton and Columbus.