The former Plymouth man had been linked with Newcastle, Sunderland and QPR.
Williams, 23, moves for a fee which is understood to be £50,000 and has signed a deal that ties him to the club until the end of next season.
The former Winchester City and AFC Totton man, who has scored eight goals in the Blue Square Bet Premier for Eastleigh this season, has been training with Reading for the past week.
Source: BBC Sport
Source: BBC Sport