The former Blackburn Rovers striker quit as North Shields boss earlier today after four and a half years in charge of the Robins.
Fenton will share the managerial duties with former assistant boss Picton, after Jon King's shock sacking yesterday.
Shields are third top of the Northern League, level on points with leaders Shildon, after a fine start to the season.
Man in life-threatening condition after 'serious collision' involving car and pedestrian in South Shields
Campaigners rally against Local Plan after farmland in Cleadon earmarked for 156 homes
Appeal to find owner of lost Labrador after dog found near Jarrow Cemetery
Pair set up cannabis farm in town centre flat
South Shields man jailed for terrifying physical and sexual assault on woman in her own home
A club statement said: "Graham Fenton and Lee Picton have been appointed as joint managers of South Shields.
"Lee steps up from his role as assistant manager at the club, while Graham joins following a hugely successful four-and-a-half-year spell in charge of North Shields.
"At Daren Persson Stadium, Graham achieved promotion from Northern League Division Two and steered the Robins to two top-five finishes in Division One.
"His North Shields side also memorably won the FA Vase at Wembley in 2015, while in his playing days, Graham was a much-respected professional with the likes of Aston Villa, Blackburn Rovers and Leicester City.
"In addition, the club can confirm that it is in ongoing dialogue with Jon King regarding a possible revised role within the club, and hopes an agreement can be reached."
Fenton and Picton are work colleagues, both coaching football at Monkseaton College.