The 19-year-old, who has represented Scotland at youth levels, could make his debut for Shields in Saturday's BetVictor Northern Premier League Premier Division game against Hyde United at Mariners Park.
Connelly joins fellow Sunderland youngster Jordan Hunter in making a loan switch to the Mariners.
He can play anywhere across the forward line and made his debut for the Black Cats' first team in the EFL Cup last October.
South Shields joint-manager Graham Fenton said: "We have watched Lee on a number of occasions and have been really impressed with him over the last 12 months.
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"We have been particularly impressed with his work ethic, awareness of spaces and well-timed movements, as well as his finishing ability.
"He is a versatile forward who can play across all three front positions, and we're delighted to bring him on board to bolster the squad in this early part of the season when we have so many games coming thick and fast."
The striker is the second Sunderland player to join South Shields on loan.
Earlier this week, Hunter also arrived on a 28-day youth loan. The 19-year-old right-back came on as a second-half substitute for the Black Cats in July's pre-season friendly between the sides at Mariners Park.
Picton said: "He is a player we have watched on a number of occasions and we feel he will strengthen our squad heading into a period when we will play a lot of games in a short period of time."
The Mariners have won both of their opening two fixtures to take their place at the top of the early Northern Premier League Premier Division table, but could be without a number of key players against Hyde.
They will find out today whether their appeal against the red card picked up by Jason Gilchrist in last Saturday's season opener at Radcliffe has been successful.
They are also without Jon Shaw (hamstring) and Craig Baxter (hernia), with doubts over Luke Daly (knee), Dillon Morse (dead leg), Blair Adams (groin) and David Foley (groin).