26-year-old Webster traveled the United States to sign the contract and will remain there for a three-day training camp during the NBA preseason.
"If I can do enough to impress the coaches and the players that are here and prove to them that it's not too much of a risk to to put me on that team then I can make that contract guaranteed," he told the Crowd Goes Wild Breakfast.
"I'm just working hard up until training camp and then when that starts I think that's the real time to prove myself, so I'm just getting ready for that."
With two roster spots available, Webster is competing against four other players for a place on the team.
"We all bring a different type of game," he said.
"It just depends on what they're looking for. The word is they're looking for an outside shooter which I think I can fill the mold for what they're looking for."
The opportunity to earn a spot with the Pelicans "means the world" to Webster, who has dreamed of playing in the NBA since he was a child.
"I haven't taken the easiest road to get here, it's taken a long time but I finally have," he said.
"I've never given up on my dream. I'm working as hard as possible, leaving it all out on the floor in the hopes of getting to the NBA."
