The 22-year-old Dixon, who made 20 appearances for Saints in 2012, linked up with his old back-row partner Matty Ashurst for the start of pre-season training this week.
"Andrew will do well for us," Reds coach Phil Veivers said. "He has a wealth of Super League experience from his time at St Helens, he's young and hard-running. He will fit in well with what we are trying to achieve next season."
Salford have lost seven members of last season's squad and Dixon is expected to be the first of at least five new faces once the club's proposed takeover is completed.