The 27-year-old agreed a one-year contract after leaving Accrington Stanley as a free agent at the end of last season.
Dundee have already signed Scott Allan, Glen Kamara, Lewis Spence, Sofien Moussa, Jack Hendry, Roarie Deacon and Randy Wolters.
Parish will challenge number one Scott Bain for a starting place in goal.
A graduate of Aston Villa's youth set up, and a former England under-20 international, Parish impressed Dundee manager Neil McCann during a trial spell.
After spells at Cardiff, Wycombe, Bristol City, Newport County, Blackpool and Colchester, Parish made 16 appearances for Accrington Stanley last season.
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Dundee have made goalkeeper Elliot Parish their eighth signing of the summer.