Winning a mandate, with 158 of 300 seats in Parliament, Mitsotakis avoided having to bring in a coalition partner, which most likely would have been KINAL.
The incoming government's promise to lower taxes and calls to ease the strict budget targets was bluntly rejected by Greece's creditors even before the new ministers had been sworn in.
Euro area finance ministers meeting hours later in Brussels said key targets already agreed with Athens would not be changed.
Mitsotakis, whose late father, Constantine Mitsotakis, was a conservative prime minister in the early 1990s, has promised to make Greece more business-friendly by lowering taxes and cutting red tape.
"(Jean-Claude) Juncker assured the incoming government that they can continue counting in their full support to ensure that the country and its people will live with the full benefits of the efforts that were undertaken in recent years", said the European Commission's Deputy spokesperson, Mina Andreeva.
Mitsotakis's new Cabinet will rely heavily on experienced politicians who served in previous conservative governments.
Greece depended for eight years on rescue loans from other European Union countries and the International Monetary Fund in return for deep reforms to the country's economy that included steep tax hikes and major spending cuts.
One of the key figures in the cabinet is Christos Staikouras, who was sworn in as Finance Minister on Tuesday.
Unemployment and poverty levels soared in the country. Critics say that requirement has shackled government spending and stifled the country's recovery.
"We will maintain any positive things that were done and we will build on them", he said.
"We will see more in detail in the Finnish Eurogroup in September, of course, there will be an EWG before that, but for the moment I cannot say more", the official added, admitting that "all political parties have challenged the 3.5% target and we would have this problem anyway, whoever won the election, but I repeat, is part of the 2018 package". Nikos Dendias, the new foreign minister, held previous Cabinet posts at the ministries of public order, development, and defense.