The 33-year-old – who can operate in the middle of the park or as a striker – began his career with Leicester City and had loan spells with Rochdale and Lincoln City.
Dodds then made a permanent switch to Port Vale where he spent eight years, making 289 appearances and scoring 51 goals.
He then joined Salop and spent two seasons at Montgomery Waters Meadow before moving on to Chesterfield and then a loan spell back at Port Vale.
After dropping down to the National League last season with Chorley, who finished bottom of the table, Dodds has now signed on with Southern Premier Central side Hednesford.
“I’m excited to be here at Hednesford,” Dodds said.
“The ground is as good as many in the National League and I have been impressed with the plans for the club. I know a few of the lads such as Danny Glover and I’m looking forward to getting started.”