Prop forward Sidlow, 25, has become the Bulls' fourth recruit, following the arrival of Jamie Foster, Ben Evans and Matty Blythe, after signing a two-year deal.
Salford, who are desperately seeking new investment as they battle against a winding-up petitition, agreed to release Sidlow from the 12 months left on his contract with them.
"I really enjoyed myself at Salford but this is a big step up in my eyes and I'm looking forward to the challenge here," said Sidlow.
"I'd like to thank Steve Simms and John Wilkinson at Salford because they have both been brilliant in letting me go.
"They said that if Bradford had a longer-term deal for me, then they would not stand in my way. I felt the security of being at Bradford for the next two years was a big step up for me."
The capture of the 6ft 4in, 17st Sidlow will help offset the departure of Tom Burgess, Craig Kopczak, Bryn Hargreaves and Olivier Elima from Bradford's 2012 squad.
"Adam is a big lad," said Bulls coach Francis Cummins. "He can get forward and he's got a great offload as well so he brings another dimension to our attack.
"We've been trying to sign Adam for a while and it has taken some time but he's here now and I'm really pleased we've got our man."