There are various options:
On Linux you can use the grib_copy tool. This tools comes with ECMWF's ecCodes:
grib_copy grib_file_1 grib_file_1 ... 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
