There are various options:

For GRIB:

On Linux you can use the grib_copy tool. This tools comes with ECMWF's ecCodes:

grib_copy grib_file_1 grib_file_2 ... output_grib_file

On Linux you can simply concatenate the GRIB files:

cat grib_file_1 grib_file_2 ... grib_file_N > output_grib_file

For NerCDF (unsupported by ECMWF)

You can use CDO merge:

  cdo merge infile1 infile2 infile3 outfile

or

  cdo mergetime infile1 infile2 infile3 infile4 outfile