Bird, 25, enjoyed a prolific 2012/13 season in the Southern Premier League, netting an impressive 45 goals in 42 games.
The Slough-born forward has already featured twice for Guy Whittingham's side in pre-season, scoring twice on his debut against Havant & Waterlooville.
"It's unbelievable," he told the club's official website. "I'm having to pinch myself because it's a dream come true.
"I was working on a building site a few weeks ago and this is obviously a lot better!
"All the lads have made me feel very welcome and it was great to get a couple of goals in my first game. The first one was a bit flukey, but I also hit the post, so it was a shame I couldn't get a hat-trick."
He added: "It's a big step up for me and it's a risk for the manager to take me on, but I'm confident in my ability to do well at this level.
"I have to thank Guy Whittingham and Steve Allen. They've both shown a lot of faith in me and I'm determined to repay them."