The 48-year-old had taken charge on an interim basis for Trabzonspor’s final two games of the season after the departure of Huseyin Cimsir and oversaw a 2-0 win over Alanyaspor in the Cup final to land the club’s first trophy in a decade.
Trabzonspor confirmed Newton's appointment as their manager in a statement on Sunday but did not give details of the length of his contract.
Newton had told Sky Sports after Trabzonspor’s triumph that a lack of opportunities in England had prompted him to seek a job abroad.
“I’ve been trying to become a number one for a while and just didn’t see it happening”, he said.
“The fact is I’ve moved to another country and it’s taken six months to become caretaker manager ... I’ve been working in football all my life so that’s why I felt there was more opportunity here, so I had to take the chance, basically.”
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After nine years as a Chelsea player, Newton spent a further eight years as a coach in the club and was assistant to Italian Roberto Di Matteo when they claimed the Champions League and FA Cup titles in 2012.
He had reprised that role under Dutchman Guus Hiddink in 2015 and moved to Turkey in February this year to work as Cimsir’s assistant.
Trabzonspor finished second in the Super Lig behind Istanbul Basaksehir.
But the club lost their place in next season’s Champions League after the Court of Arbitration for Sport dismissed their appeal against a one-season ban imposed by UEFA.