We consider a composite Higgs model embedded into a Grand Unified Theory (GUT) based on the $E_6$ gauge group. The phenomenological viability of this $E_6$ inspired composite Higgs model (E$_6$CHM) implies that standard model (SM) elementary fermions with
different baryon or lepton number should stem from different $27$ representations of $E_6$. We present a six--dimensional orbifold GUT model in which the $E_6$ gauge symmetry is broken to the SM gauge group so that the appropriate splitting of the bulk $27$--plets takes place. In this model the strongly coupled sector is localised on one of the branes and possesses an $SU(6)$ global symmetry that contains the $SU(3)_C\times SU(2)_W\times U(1)_Y$ subgroup. In this case the approximate gauge coupling unification can be attained if the right--handed top quark is a composite state and the elementary sector involves extra exotic matter beyond the SM which ensures anomaly cancellation.
The breakdown of the approximate $SU(6)$ symmetry at low energies in this model results in a set of the pseudo--Nambu--Goldstone states which include a Higgs doublet and scalar colour triplet. The presence of the TeV scale vector--like exotic quarks and scalar colour triplet may provide spectacular new physics signals that can be observed at the LHC. The possible interpretation of the 750 GeV diphoton excess within this composite Higgs model is also discussed.