All three will form part of Warriors' new-look squad which Director of Rugby Dean Ryan is building ahead of next season.
Annett said: "I have hugely enjoyed my time with Ulster and really appreciate the opportunity that David Humphreys and Ulster Rugby have given me. I am ambitious and feel I really need to push on. With what Worcester have got planned, plus their prospects for the next couple of years, it is a very exciting place to be joining.
Six-foot-eight lock Sanderson moved to Moseley in 2011 before joining Rotherham a year later and has gone on to make 45 appearances for his current club.
Sanderson said: "I'm excited to be joining Worcester and I'm looking forward to the challenges ahead.
"The set-up is first-class and Dean's enthusiasm for the club really convinced me that this was the place to be. This is a big club with ambitions that match mine and I'm proud to be a part of it."
Hooker Sowrey joined Rotherham at the start of this season and has gone on to make 18 appearances for the club.
Sowrey said: "When I came down to Worcester for discussions I really bought into Dean's vision for how the club will move forward.
"I'm looking forward to being part of the club's future and developing under people like Carl Hogg and Nick Johnston.
"I've enjoyed my time at Rotherham and am grateful to all the staff for their support during my time there. I'm ambitious to make the number two jersey my own at Worcester and cannot wait to get started."
Warriors Director of Rugby Dean Ryan said: "I am delighted that one of the best young forwards in Ireland has decided to join us alongside two of the brightest talents in the Championship.
"Niall has developed well at one of the strongest teams in the PRO12, while Dan and Ben have been key performers for a club which is battling to win the Championship title."