Brandy, Stephen McGinn, Sean McGinty and Jasper Johns have all been unveiled at Bramall Lane as Weir begins to shape his squad for the forthcoming League One campaign.
Striker Brandy, who scored seven times for Walsall last season, has signed on a two-year contract along with versatile Scotsman McGinn who scored against the Blades last season while on loan from Watford at Shrewsbury.
McGinty, 19, has also penned a two-year deal having departed Manchester United.
Another player to leave the top flight is ex-Everton midfielder Johns who has signed a one-year deal and will begin in United's development squad.
New boss Weir told the club's official website: "We are delighted that deals for all four of the lads have been completed in time for them to start pre-season training with the rest of the squad and we are confident that we can develop their talents, individually and collectively, for the benefit of Sheffield United."
The Blades have retained the option to extend all four contracts for a further year.