The versatile forward, one of England’s brightest attacking prospects, will initially stay at St. Andrew’s until 12 January with the ability to extend the deal further should all three parties agree.
The 19-year-old is a product of the West Ham United Academy and broke into the Hammers’ first-team squad last season. The Aylesbury-born talent was named West Ham’s Academy Player of the Year for 2011/12 and also enjoyed loan spells at Oxford United and MK Dons.
The England Under-19 international represented his county at the 2010 UEFA European U17 Championship and also helped the Three Lions progress to the semi-finals of the 2012 UEFA European U19 Championship.
Predominately a left winger, Hall has been given Blues first-team squad number 29 and is eligible for this Saturday's trip to Derby County.
Following Hall's capture, Blues boss Lee Clark told bcfc.com: "Rob is a very quick-footed attacker who has got great ability to go past defenders and creates great opportunities for himself and others.
"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 Barclays 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."
To date, Hall has made seven first-team appearances for West Ham, six as a substitute, and his parent club will have the option to recall the player after a period of 28 days.