The 34-year-old had been training with the club in recent weeks before agreeing to the deal.
Borini was most recently with Sampdoria, where he spent two seasons in Serie B before leaving in the summer.
“It's been great," the Italian said. "I came in to train to keep myself fit while between contracts, and the gaffer let me use the facilities.
“I’ve never played in League Two, so I’ll learn from my teammates, but I’ll bring experience and try to lead by example. I needed real football again and I’m embracing the challenge.”
Borini began his career at Bologna before joining Chelsea’s academy in 2007 as a teenager.
After a successful spell with Roma, he moved to Liverpool in 2012, later finding regular football at Sunderland.
He went on to play for Milan, Hellas Verona and Turkish side Karagumruk before joining Sampdoria.
Borini, who will wear number 16, is expected to be available for Salford’s next fixture, against Oldham on 18 October.