The new leadership group Netanyahu presented to Peres will be sworn in at the Knesset Monday, The Jerusalem Post reported.
"As you know, I formed a government. You gave me the mission, and I accomplished it," Netanyahu told Peres.
"We are facing a decisive year in security, the economy and efforts to promote peace, as well as the desire of Israeli citizens to bring change."
Peres congratulated Netanyahu on creating the coalition on time.
U.S. President Barack Obama Saturday also sent along his congratulations.
The White House issued a statement by press secretary Jay Carney saying the president "looks forward to working closely with the prime minister and the new government to address the many challenges we face and advance our shared interest in peace and security."
"The United States places a high value on its deep and enduring bonds with Israel and the Israeli people," the statement said. "The president looks forward to further strengthening those bonds when he travels to Israel next week to meet with Israeli officials and to speak directly with the Israeli people."
Under the new Cabinet, Transportation Minister Israel Katz and Culture and Sport Minister Limor Livnat will stay in their current posts while Strategic Affairs Minister Moshe Ya'alon will become defense minister, the Post said. Education Minister Gideon Sa'ar may become the Interior Ministry, though Gilad Erdan also is under consideration.
Knesset Member Yariv Levin was offered the position of coalition chairman, but he had yet to agree, the Post said.
Avigdor Liberman will return as foreign minister if exonerated in his corruption trial, the newspaper said.
Netanyahu remains prime minister after an agreement was reached Friday to create a 68-member coalition that includes members of his Likud Beytenu party, the centrist Yesh Atid and "The Movement" parties, and the Jewish Home Party, which supports the expansion of Jewish settlements in the Palestinian West Bank territory.