Grounds agreed a two-year deal with Birmingham earlier this week after leaving Oldham Athletic and he will be joined at St Andrew's next season by Hall.
The 22-year-old has yet to make a first-team appearance for Tottenham after joining from Brighton in 2012 and he featured 34 times on loan at Swindon Town last season.
Hall will be able to spend the full season with Birmingham and manager Lee Clark is happy to have made early moves in the transfer market to improve his defence.
"I've got to stress that a big reason we were prepared to do this loan deal was due to the fact that there can be no recall so Grant is effectively our player for the next year," Clark told the club's official website.
"I watched him closely at Swindon Town last season and he impressed before picking up a hamstring injury. I know that (Swindon manager) Mark Cooper speaks very highly of him and we were actually in for Grant last season but due to the link between Tottenham and Swindon it didn't work out for us.
"We're delighted to have Grant on board and it's no coincidence that my first two signings have been defenders because that was an area we needed to address.
"We simply didn't keep enough clean sheets last season and, as we look to continue to improve that area, there will be more defenders to come."