The 42-year-old Argentinian returns to the 1st Cloud Arena five years after ending his playing career there with 120 appearances, six trophies and three promotions.
He replaces former England international Phillips, who guided the Mariners to the Northern Premier League title before leaving the club by mutual consent earlier this month.
Arca, who captained Shields to a quadruple which included the FA Vase in 2016-17, said: “It’s great to be back at the club after so many years.
“I firmly believe this is the right time for me to come back for a different challenge, and I’m very excited about it.
“The club has grown so fast and this is a fantastic opportunity for me to become a manager for the first time, especially with the platform we have here.
“There is a lot of work to do between now and the start of pre-season, but I’m very hungry to get started and help the club continue to progress.
“I like to compete. I’m not a person who is happy to sit in mid-table, and that’s why we need to get the right things done at the beginning. I will do the best I can to put South Shields in a great position next season.”
Arca began his career at home with Argentinos Juniors before making a total of 362 appearances for Sunderland and Middlesbrough following his move to England as a teenager.
He won new admirers after being coaxed back onto the pitch by South Shields, where he spent three hugely-successful years before hanging up his boots for good.
Chairman Geoff Thompson said: “We are thrilled to welcome Julio back to the club and to provide him with his first opportunity as a manager.
“It’s a hugely exciting time for the club and with Julio now installed, we are ready to finalise our plans for the season ahead in National League North.”