The promising centre back will follow in the footsteps of former League of Ireland players in making the move to Berkshire
The 17-year-old has made the breakthrough to the first team picture at the Carlisle Grounds this season, playing 12 games for Pat Devlin's side in defence.
A representative of Ireland's under-age teams, Sweeney will now follow in the footsteps of Kevin Doyle and Shane Long in making the move to the Royals from the League of Ireland.
He joined Bray from Belvedere last season and has impressed in his debut campaign, also reportedly alerting Everton to his potential.
The move is expected to be formalised on Thursday.