Full-back Beye arrived in a £2.5million deal from Newcastle United with 19-year-old midfielder Delph costing around £6million from Leeds.
Villa's other summer signing, winger Stewart Downing who cost £12million from Middlesbrough, will be sidelined until December by a broken foot.
But Villa are set to be boosted by the return of midfielder Stiliyan Petrov who dislocated his shoulder in The Peace Cup against Atlante in Spain last month.
Petrov is also in the running to become the club's new captain following the retirement of Martin Laursen and departure of Gareth Barry.
Villa (from) Friedel, Guzan, Beye, Luke Young, Davies, Cuellar, Shorey, Milner, Reo-Coker, Sidwell, Delph, Ashley Young, Heskey, Carew, Agbonlahor, Lichaj, Clark, Albrighton, Lowry, Gardner, Delfouneso.