The Republic of Ireland U21 international joined the Hammers from NIFL Premiership side Cliftonville in 2023.
Now 19, Moore leaves West Ham in a permanent transfer.
He joins Shelbourne ahead of their UEFA Champions League second qualifying round, second-leg tie against Qarabağ.
Moore told the club's website: “I’m absolutely buzzing to be here. Shelbourne is a massive club and I’m delighted to get the deal done. I’m ready to get to work, hit the ground running, and show the fans what I’m all about.”
Joey O’Brien, Shelbourne FC manager said: “Sean’s a top young player with huge potential. He came into the game at a young age with Cliftonville and earned a great education over in England with West Ham.
"Now he’s ready to kick on with the next stage of his career, and we’re delighted he’s put his trust in us. He’s an exciting player to watch, really positive in how he plays the game. He can play in multiple positions on both sides of the pitch, which gives us great flexibility.”
Luke Byrne, Shelbourne FC Technical Director said: “Sean is a really exciting talent with lots of potential and we are looking forward to working with him to develop that talent. He is a young Irish player who definitely fits the profile that we want to add to the squad. We’re very happy he has chosen Shelbourne as the best place to continue his career.”