Byrd spent five seasons with the Buffalo Bills until he joined the Saints last month, but he never experienced a season in which his team won more than six games and has never appeared in the playoffs.
Having signed a six-year, $54m (£32.1m) deal with the Saints, Byrd has stated that he can't wait to get started and help the team reach the post-season.
Speaking at a charity event, Byrd said: "You hear so much about the organisation and how great it is. But to be here, get to meet the people that run the organisation; it's great. It's first class.
"When you prepare at a high level and you don't see the fruits of your labour, that's a tough thing. I'm certainly looking forward to winning a lot of games with the Saints. I'm prepared for this."
Byrd has been chosen for the Pro Bowl on three occasions and has been named the AFC interceptions leader twice.