The 23-year-old striker has signed a one-and-a-half-year contract at the Madejski Stadium following a transfer from non-league Eastleigh.
Speaking to the Southern Daily Echo, Williams said: "I've got butterflies.
"I sat down with Sir John Madejski, signed all the paperwork and then I was given my shirt and taken onto the pitch for photos with manager Brian McDermott.
"I'm a bit overwhelmed by it all, but it's really exciting."
Williams, who scored eight goals in 14 starts for Eastleigh, joins for an undisclosed fee and will be available to face Hull on Saturday.