The much talked about trade was a little while in coming but was completed on Tuesday morning, with the Bulldogs acquiescing to the Swans' demand for a third-round draft pick.
The clubs will also swap two later draft picks as part of the deal, with details to be confirmed later in the exchange period.
A clearly relieved Hall said he had feared the negotiations would stretch throughout the week.
"It was a tense couple of days. I thought it would get done with a couple of minutes to go on Friday", he said.
"The uncertainty is gone and we can look forward to setting up down here and cracking into training.
"The hard work starts now."
Coach Rodney Eade believes Hall will add more to the team than just an avenue to goal.
"It's a great result," he said. "A player of Barry's quality - I think what he brings to the group is more than just his playing ability, his experience and the way he can play.
"He's such a team-orientated person. I think he can mentor our young forwards as well so there's a dual role there for him. It's certainly pleasing to get it done early in the week."
Eade also said there had been no movement on re-signing full-back Brian Lake although the club remains confident he will stay with the Bulldogs
More to follow.
The 2009 AFL exchange period runs from October 5-9. No trades are official until paperwork has been accepted by the AFL and formally recognised after 2pm on Friday, October 9
