Sterry, 24, came through the ranks at Newcastle United and made 12 senior appearances for the club before leaving at the end of last season.
He has also featured at Coventry City and Crewe Alexandra.
Hindle, 26, joins on loan from League Two side Barrow until the end of the year.
Sterry was named in the starting line-up in their FA Cup clash, while Hindle was named on the bench.
South Shields joint manager Graham Fenton said: “We’re absolutely delighted to welcome both players to the club.
“Jamie has been training with us for a prolonged period and we are extremely pleased that he has committed to joining the club.
“He has a strong pedigree in terms of the clubs he has played for and has really impressed myself, Lee Picton and Brian Smith during training sessions over the past couple of months, so we feel fortunate to have him as part of our squad.
“We’re equally delighted to have signed Jack on loan from Barrow.
“He is someone we have kept an eye on since he played against us for Colwyn Bay three years ago and he has gone on to play games and score goals at National League level.
“He can play anywhere across the front line and will provide us with even more competition for places at the top end of the pitch."
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