Left-sided defender Hart, 23, became Sam Ricketts' first signing of the January window as he checked in on loan from Blackburn on Friday after Ryan Giles was recalled by Wolves.
He was on the bench for Saturday's 2-2 League One draw at Fleetwood and could make his Shrewsbury debut against the side he grew up supporting and represented at youth level.
Hart, from Bolton, was even given a senior Reds debut by Jurgen Klopp in a friendly at the German boss' former club Mainz in 2016.
But, after leaving the Anfield club to join Championship Rovers in 2017, Hart is now looking to shine in blue and amber.
"It's been a bit of a whirlwind but I'm really excited to be here and see what the next couple of months hold," said Hart, who has played on loan in League One with Port Vale, Rochdale and Southend.
"It was very quick. Giles was here and that happened quick. I got pulled by the Blackburn manager on Friday morning and he said 'what are your thoughts about going to Shrewsbury?'
"I thought it'd be an amazing move for me. It's quite local so it's perfect and I'm really excited.
"The lads are a lovely bunch, I've only been around them about 24 hours and it helped staying in the hotel (before Fleetwood) to meet them properly and be around the group.
"I thought we could've kicked on to get three points but I obviously hope to be in there from next week.
"On a different day we could've got a win but Fleetwood are a right group – we can kick on now.
"I don't really mind (where I play) as long as I'm playing. I'm left footed so I prefer the left but left full-back or left wing-back I'm happy with both.
"I've played in League One a couple of times with various clubs and I'm hoping to make a name for myself at Shrewsbury."
Hart was a junior at Manchester United before joining Liverpool as a 16-year-old.
On the prospect of joining Salop shortly before their mouth-watering FA Cup tie with the Reds, the full-back added: "It's crazy. The first thing the gaffer told me at Blackburn was they're playing Liverpool next week and it'll be nice to see a couple of old friends.
"I'll be ready for it and hopefully get the shirt to play.
"It would be amazing. I grew up playing there so to put the shirt on again would be amazing for me and my family.
"I was there for four years. I loved my time and learned a lot from the staff, I've got a lot of friends and moved on to Blackburn two years ago."