The 21-year-old, brother of Crystal Palace's Darren, signed a four-year deal and becomes Adams' fifth new signing of the summer.
Adams speaking from Cyprus where he is on holiday commented on the latest capture: "In Elliott, we have a young, talented and confident defender who I'm sure will bring a real presence to our back line.”
"He is just the sort of player we are looking for to help the club progress and I'm delighted that the Board and senior management team have supported me in spending the money to bring him in. I have no doubt that he will be a valuable addition to our squad."