The French front-row came through the ranks at St Helens - playing alongside Danny Richardson and Regan Grace in their 2016 Academy Grand Final winning side - before spending a season with NRL club Melbourne Storm.
Congo-born Nzoungou, 20, then moved to Toulouse Olympique before joining Salford this term.
He made his Super League debut earlier this year against Wigan and also spent time on loan at Oldham, Whitehaven and Swinton.
Now Radford has signed him ahead of 2019 and he said: “I’m really excited to work with Levy because I think he’ll be a great player with the right time and investment.
“The reserves will give him a good opportunity to play consistent rugby league next season, which will hopefully help in his development to push for a regular place in the first-team.
“He adds more valuable depth to our squad and is one to watch.”
Nzoungou added: “I’ve come to Hull FC to settle down, work hard and make the most of the opportunity.
“I have had good experience at a number of clubs so far, but I would like to come here and stay for as many years as possible and become a key part of the team.
“It is a great club and everyone has been very welcoming.
“Lee has explained the opportunity for me here and how to have a spot in the squad, so I am going to work hard for it and I am determined to do well."