The Arsenal winger has joined the Bees on a season-long loan.
"I can't wait to get going," he said. "It's a big platform for me to express myself, and that's what I need right now.
"I wanted to go to a club where I know I'm going to play regularly; I know there's competition for places but I'm going to train hard and show myself that I can get the minutes I deserve."
Nelson, who spent last season on loan at Fulham, added: "I'm a player that expresses myself. I want the fans to go away thinking about a goal, an assist, or something exciting I'd done.
"I'm very passionate. It might only be a loan, but I'm going to care for the club like it's my own.
"I'm excited to get out there in front of the fans."
