Wolves winger Zeli Ismail has rejoined Burton on loan.
Southampton have signed central defender Steven Caulker on a season-long loan from QPR.
Striker Tankulic scored during Dundee's recent 2-0 friendly win over Manchester City while Konrad impressed in central defence.
Both players have agreed two-year deals with the Championship title winners after moving from the regional leagues below the third tier of German football.
Konrad, 24, previously played in the second tier with Karlsruhe while 23-year-old Tankulic has moved from Wolfsburg's second team.
Manager Paul Hartley told the club's official website: "They impressed when we were away in Hungary and in the Manchester City game showed what they can do.
"They are both at a good age and fit into squad we are building. Another two good additions."