Russia's U.N. Ambassador Vitaly Churkin, president of the15-member council for October, said he hoped the council would unanimously recommend Guterres, who was also the United Nations High Commissioner for Refugees from June 2005 to December 2015.
Guterres, 67, would replace Ban Ki-moon, 72, of South Korea, who will step down at the end of 2016 after serving two terms. Guterres was prime minister of Portugal from 1995 to 2002.
"Today after our sixth straw poll we have a clear favorite and his name is Antonio Guterres," Churkin told reporters with his 14 council colleagues standing behind him on Wednesday.
"We wish Mr. Guterres well in discharging his duties as the Secretary-General of the United Nations for the next five years," Churkin said.
The council has been holding informal secret ballots since July in a bid to reach consensus on a candidate. Members had the choices encourage, discourage or no opinion. Guterres has come out on top of all the polls and on Wednesday received 13encourage votes and two no opinion votes.
"In the end, there was just a candidate whose experience, vision, and versatility across a range of areas proved compelling," U.S. Ambassador Samantha Power told reporters.
"If we have these transnational threats and we don't have somebody at the helm of the United Nations that can mobilize coalitions, that can make the tools of this institution ... work better for people, that's going to be more pain and more suffering and more dysfunction than we can afford," she said.
Diplomats said one of the no opinion votes was cast by one of the five veto wielding powers, which are Russia, China, theUnited States, France and Britain.
The Security Council will adopt a resolution, traditionally behind closed doors, recommending that the General Assembly appoint Guterres for a five-year term from Jan. 1, 2017. The resolution needs nine votes in favor and no vetoes to pass.
"We hope it can be done by acclamation," Churkin said.
Thirteen people were nominated in the race to become the next U.N. chief, but three had already withdrawn beforeWednesday's secret ballot. In a bid for more transparency in the opaque selection process, the candidates were for the first timeable to make election campaign-style pitches to the General Assembly.
When Guterres spoke to the General Assembly in April, he said he was a candidate to become secretary-general because "the best place to address the root cause of human suffering is at the center of the U.N. system." He spoke in English, French and Spanish during the two-hour long town hall meeting.
Guterres, a devout Catholic, spoke about his decade as theU.N. refugee chief as "an extraordinary privilege but a terrible frustration because there was no humanitarian solution for their plight." He said the solution was always political.
He described a U.N. chief as "acting with humility, without arrogance, without giving lessons to anybody, but working as a convener, as a facilitator, as a catalyst and behaving like an honest broker, a bridge builder and a messenger for peace."
Seven of the candidates for secretary-general were women amid a push by civil society groups and a third of the 193 U.N.member states for the first female U.N. chief in the 71-yearhistory of the world body, which has had eight male leaders.
The Woman SG lobby group described the win by Guterres as "a disaster for equal rights and gender equality" and said it wasan outrage that it appeared the female candidates were "never seriously considered."
In April, Guterres pledged to present a roadmap for gender parity at all levels of the United Nations if elected.
Britain's U.N. Ambassador Matthew Rycroft paid tribute to all the candidates and in particular the women.
"Although it's high time for a woman ... the most important thing for the UK was the qualities of leadership of this position," he told reporters.
He said Guterres was the person to "provide a convening power and a moral authority at a time when the world is divided on issues, above all like Syria."
The U.N. Director at Human Rights Watch, Louis Charbonneau, said: "Ultimately, the next U.N. secretary-general will be judged on his ability to stand up to the very powers that just selected him, whether on Syria, Yemen, South Sudan, the refugee crisis, climate change or any other problem that comes his way."