The 29-year-old utility forward has followed his international team-mate Sam Luckley to the AJ Bell Stadium.
Addy, formerly of Leigh, Hull KR and Bradford, said: “I’m buzzing to be joining Salford and can’t wait to get started. It’s already a good squad and I want to add to it.
“Obviously I was captain at Leigh. I see myself as a leader, whether captain or not, so will look to show that here.”
Salford head coach Richard Marshall added: “Danny is another player whose versatility presents us with a number of exciting options going into next season.
“In him, we’ve also added another leader to our group, which helps create the right environment for some of our younger recruits.”
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