For a general H2 optimal control problem, at first all H2 optimal measurement feedback controllers are characterized and parameterized, and then attention is focused on controllers with observer-based architecture. Both full-order as well as reduced-order observer-based H2 optimal controllers are characterized and parameterized. Also, systematic methods of designing them are presented. An important problem, coined as an H2 optimal control problem with simultaneous pole placement, is formulated and solved. That is, since in general there exist many H2 optimal measurement feedback controllers, utilizing such flexibility and freedom, we can solve the problem of simultaneously placing the closed-loop poles at desirable locations whenever possible while still preserving H2 optimality. All the design algorithms developed here are easily computer implementable.