Blender open-source 3D computer graphics software supports 3D graphics saved in OBJ files just fine, so you can simply import them to the program, work on them and produce a .blend file via export function. Seems the obvious choice for this conversion.
Convert 3D object graphics to Blender 3D data file.
We have found 3 software records in our database eligible for .obj to .blend file format conversion.
Microsoft Windows software - convert obj to blend on Windows
A very popular free program used for work with 3D graphics
Convert from obj file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned obj to blend. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert obj to blend on OS X
The Mac version of popular free 3D graphics software
Linux/Unix software - convert obj to blend on Linux
Easy-to-use 3D modeling utility