The 19-year old striker has signed a loan deal which will run until January 12 and Brum boss Lee Clark is excited about having the talented forward at his disposal.
"Rob is a very quick-footed attacker who has got great ability to go past defenders and creates great opportunities for himself and others," Clark said of Hall who has recent loan spells with MK Dons and Oxford United.
"He's also got a great strike of the ball so I'm looking forward to working with him and he's excited about the challenge.
"It was quite a coup getting Rob because he's been doing really well in the development squad at West Ham which has got him on the bench for most of the season in the Premier League.
"I have got to thank Sam Allardyce for allowing this one to happen. In all honesty, I didn't think he'd allow Rob to come as he's been a big part of their squad but thankfully he has. We're now looking forward to working with him."