The 31-year-old signs a two-and-a-half-year deal at the Peninsula Stadium after two seasons with the Imps.
Green is no stranger to the National League, winning the title twice with Oxford United in 2010 and then again with Mansfield Town in 2013 and he hopes to make it third time lucky with the Ammies.
“Ambition is totally, 100% promotion, that’s what I’ve come here for this season," he told the club's official website.
“It’s a refreshing challenge for me and I’m really looking forward to getting started, meeting my new team mates, and hopefully being part of a promotion winning team.
"I’m a very ambitious lad and I saw a great opportunity at Salford City and I’m really looking forward to getting started.
"I know it’s been very tight at the top with points and I’m just hoping I can add to what the lads have done so far and get behind them."
Green could be in line to make his debut against Dagenham & Redbridge this Saturday.