How can I blend / flllet two objects of different shape? I have two objects of different shapes with complex forms but they can be approximated with something like this:



How can I make that the "cube" blends nicely into the cone (sometimes this is called filleting)?

I tried with metaballs but these don't work on different shapes. Also I tried to sculpt but it cannot be done very precisely and symmetrically.

Any advice would be appreciated.
Increase vertex density and Loop Tools Circle, Bridge



Various Stages of Editing.


Cube in Edit mode, Loop Cut on twice in X and Y Planes.  Delete Middle Squares of vertices
Think about vertex count of target Cylinder
Select Perimeter of hole and Loop Tools Circle in Tool Panel
Extrude in Z Axis
Loop Cut and Shape with Proportional Edit 
The result is compatible with another Cylinder with same vertex count.
The Cylinder is not shown above, [Join] two separate objects if necessary
Use Bridge Tool to connect to perimeter of Cylinder
Bridge examples can be found by searching here at BSE