The full-back had been linked with a move to Hull City but Martin O'Neill has pounced with the offer of Europa League football this season.
Beye, 31, has cost the Claret and Blue around £2.5m and he is likely to go straight into the side for the season opener at Villa Park against Wigan next weekend as regular right-back Luke Young is injured.
Beye will also provide cover at centre-back for Curtis Davies and Carlos Cuellar.