Hamilton have confirmed three new signings on their first day of pre-season training.
Smith, 20, was released by Dunfermline in the summer after netting six goals on loan for Airdrie last season.
Canada international Trafford, 28, recently left Inverness, while 26-year-old Callachan was released by St Johnstone following a loan spell at Dundee.
Head coach Brian Rice told the club's website: "Callum Smith is a young player who I've been watching for a few years. He had a fantastic season at Airdrie, so I think he has a chance here. He's a worker and that's everything we're all about at Hamilton.
"Charlie I know from my time at Inverness, so I know exactly what I'm getting. He's a disciplined midfielder, a role we needed to fill and he fits the profile. I didn't want to take a chance on this position and sign someone I've only seen play a couple of times, I know what I'm getting from Charlie.
"Ross is a player I have also been watching a while, he's a box-to-box midfielder who gets in the box and scores goals – there's not many of them going about. He's one of these players that will clear a ball at one end and score in the other. I believe Ross is one the fans will take to."