Henshall, 19, has been with City for three years since joining from Swindon and spent the last five months of last season on loan at Chesterfield.
He will complete a move to the Pirates once the paperwork is completed on Thursday afternoon.
American youth international Packwood, 20, can play in defence or midfield and came through the Birmingham academy before making his first-team breakthrough last season and signing a one-year contract extension in the summer of 2013.
Manager John Ward told the club's official website: "We have got two young players in to complement the squad.
"Alex is a Swindon boy, so he knows this part of the world, and he is looking for an opportunity to get going.
"Will is highly rated at Birmingham, so much so that they don't want him cup tied.
"There is not huge experience in the boys, but they complement the group and they want to be here and want to get going and enhance their own careers as well as help us.
"New faces in a football club tend to give the whole group a bit of a lift, so I am looking for these next two days to be very positive."
- Sports & Recreation