The Hurricanes announced the deal Tuesday, a few hours before their game against Washington.
The 32-year-old Bergeron is a 10-year veteran who gives Carolina's defensive corps some depth at both ends of the ice.
He led the Lightning's defencemen with 24 points, including nine on the power play, last season and has one goal and four assists this year.
Hall returns to Tampa Bay — which put him on waivers last month. The Hurricanes claimed him March 16 and he didn't score and was a minus-2 in six games with Carolina.
The Lightning also receive the Hurricanes' seventh round pick in this June's draft.