Finely shred the peel from orange and lemon. Remove the remaining peel with a sharp knife and discard. Cut orange and lemon into wedges; discard any seeds. Core apple and cut into chunks.
Place fruit in a food processor. Add sugar. Cover and process with several on/off turns until coarsely chopped. Add cranberries. Cover and process with on/off turns until chopped. Transfer mixture to a medium bowl.
Cover and let stand at room temperature for 30 to 45 minutes before serving, stirring occasionally. Store in the refrigerator for up to 5 days.