The 55-year-old Portuguese national was officially presented to the media in Athens on Friday, a day after signing a two-year deal to succeed Rehhagel.
"The national team have had a great run over the last eight years and our goal is to continue this excellent work," the former PAOK Salonika coach told reporters.
"One era has come full circle and another one is now starting for the team."
In 2001, the 71-year-old Rehhagel took charge of a team in disarray but quickly guided the side through its most successful ever period, culminating in a stunning Euro 2004 victory which earned him the title 'King Otto' among the Greek public.
Santos is undaunted by the prospect of following in Rehhagel's footsteps and is confident he can lead Greece to more triumphs.
"I am not anxious because of previous successes... actually it makes me feel good," the former FC Porto and Benfica coach said.
"I will do everything possible to continue such success, so we have more motivation and enthusiasm to accomplish this."
Santos brings a wealth of experience of the Greek soccer scene with him, having coached some of the country's top clubs in AEK Athens, Panathinaikos and PAOK.
"I know the culture and people very well and the players know me, so this is good," Santos added.
"We will create a group of very strong and competitive players with some new elements different from my predecessor."
Santos's first match in charge will be a friendly against Serbia in Belgrade on August 11 before the Euro 2012 qualifying campaign gets underway in September.
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