The 22-year-old enjoyed a goal-laden spell with Plymouth Parkway in the Western League, winning South West Peninsula League golden boot after notching 43 times in the 2017-18 season.
Last season saw him score 19 times in 17 games for Plymouth Parkway as they finished second in the Western League.
Speaking to the club’s website, he said: "I've been speaking to Lee (Picton) and Graham (Fenton) all the way through the summer and came to the conclusion that this would be a good place for me to kick on and try to get better.
"Before I came here I had a couple of other options on the table.
"I just wanted to make the correct decision and I feel like this is the place to be.
"It's quite a long way away from home but sometimes you have to make sacrifices to try to better yourself.
"Every year I've stepped up leagues to try to better myself and now this opportunity has come up for me. My main aim has always been to play as high as I possibly can.
"I've had really good chats with Lee and he has explained the ambitions of the club, which are the same as mine."
Annear trained with his new team-mates for the first time on Friday and is available for selection in Saturday's league game against Bamber Bridge at Mariners Park.
South Shields joint manager Lee Picton said: "We're delighted to bring Jordan into the group. We've seen him play with our own eyes and for a young player, he has a good well-rounded skill set for a centre forward and ticks a lot of boxes that we are looking for.
"He has had quite a bit of interest from Football League clubs as well as clubs further up the non-league pyramid during the summer, but we have been patient and waited for our opportunity.
"Thankfully the opportunity to bring him into the squad has now come and we are really looking forward to seeing him hopefully score many goals for us moving forward."