The 28-year-old was released by Huddersfield before the transfer window closed.
Accies manager Reid said: "I have been tracking Jim for a while and I'm delighted to add him to the squad. He gives us more strength."
Goodwin - who can play in defence or midfield - has been capped by the Republic of Ireland at all levels.
He began his career with Celtic, where he spent three seasons, before moving to Stockport, Scunthorpe and Huddersfield, and had a spell on loan with Oldham last season.
Goodwin is set to be officially unveiled at a press conference later this week.