It is believed that a £500,000 deal will take him to Villa Park, with the agreement including possible add-ons should Bowery meet certain criteria.
Lambert said: "He has signed, just about. Potentially he is very good and I've got no worries about throwing him in, none whatsoever.
"It (the signing) might have surprised a few people but it is a great opportunity for him.
"He is one for the future, but if he steps up to the plate I have no fear about playing him."