Colace was named the Tykes' player of the year last season but is a free agent after rejecting a new deal at Oakwell.
And the 26-year-old is due at the Liberty for transfer talks next week with a deal almost agreed.
Swansea chairman Huw Jenkins said: "He has proved himself in the Championship with Barnsley and we think he will prove a good acquisition for us.
"We have virtually agreed terms with Hugo. The player and his agent are coming to Swansea next week to talk through the proposed agreement and hopefully to finalise things."