24-year-old Jones – who has agreed a two-year deal on Tyneside – was the Reds’ leading goalscorer last term, finding the net 19 times in all competitions.
Jones – a former Welsh U19 international – started his career with Leeds United, before taking a break from the game to travel Australia.
After returning to England, he turned out for Retford United and Heanor Town before moving to Alfreton ahead of the 2015-16 campaign.
Jones played alongside former Gateshead duo Tom Allan and Ryan Wilson last term, as the Reds finished tenth in the Vanarama National League North.
Assistant manager Lee Nogan believes Jones has the temperament to make an immediate impression at the International Stadium.
He said: “Neil Aspin has watched him play three or four times, and he has always done very well.
“He is an attack-minded player. He gets forward and he gets goals, but we’ll have a look in pre-season exactly where his best position is.
“He is a level-headed lad who wants to kick on. He’s had a taste of the Football League before, and he wants to get back there.
“He’s 24, and this is an important time for him now. There were two or three other clubs interested in him, so we’re very pleased to have him here.”