The Portuguese forward, a famously eyebrow-raising recruit towards the end of Sir Alex Ferguson's reign at Old Trafford, spent the 2015-16 season at Rayo while on the books at Benfica.
His form there persuaded Eibar to take a punt on the 27-year-old and he scored five times in 26 appearances last season.
Bebe has been more of a bit-part player for Jose Luis Mendilibar's men this time around, making 11 appearances and failing to score.
He will now join Rayo's promotion push as they aim to end a two-season absence from La Liga.
Bebe memorably joined United in a shock £7.4 million deal in 2010 and he scored twice in seven appearances for the club.
The attacker had loan spells at Besiktas, Rio Ave and Pacos Ferreira before leaving United for good in 2014 to join Benfica.