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Here's what I have been using.

Any improvements / comments are welcome.

(* this opens a notebook file and if notebook exists it CLEARS the contents as well  *)
OpenNB[fname_] := Module[{dir, fns, nb},
   dir = NotebookDirectory[];
   fns = FileNames[FileNameJoin[{dir, fname}]];
   If[fns === {}, (
     nb = CreateNotebook[];
     NotebookSave[nb, FileNameJoin[{dir, fname}]];
     ), (
     nb = NotebookOpen[fns[[1]]];
     SelectionMove[nb, All, Notebook];
     NotebookDelete[nb];
     )
    ];
   Return[nb];
   ];

(* this works for a sequence of arguments, like Print[] *)
PrintNB[nb_, args__] := Module[{boxes}, (
    If[nb === null, (
       Print[args];
       ), (
       boxes = ToBoxes /@ List[args];
       NotebookWrite[nb, Cell[BoxData[  RowBox[boxes]], "Print"]];
       )
      ];
    )
   ];

PrintNBPageBreak[nb_] := Module[{}, (
    NotebookWrite[nb, Cell["", "PageBreak"]];
    )
   ];

Here is example usage

logNB = OpenNB["ouputlog.nb"];
PrintNB[logNB, "Execution Log for: ", NotebookFileName[]];
PrintNB[logNB, "Started at: ", DateString[]];

f[r] = r^\[Gamma]*Exp[-\[Kappa] r];
PrintNB[logNB, "f(r) = ", f[r]]; 

Here is the output

Note that is you use null for the notebook argument, the output will be printed to the current executing notebook (just like Print[]).