Guterres, who was head of the UN's refugee agency for 10 years until 2015, emerged as the Security Council's runaway favorite after the latest in a series of straw polls on Wednesday.
Vitaly Churkin, the Russian ambassador to the UN and current Security Council president, told reporters that Guterres would face a vote in the Security Council on Thursday.
"Today, after our sixth straw poll we have a clear favorite, and his name is Antonio Guterres," he said.
The secretary-general of the UN is appointed in a two-stage process. A candidate is first recommended by the Security Council, and must then be approved by the 193-member General Assembly.
Thirteen candidates entered the race, necessitating a series of straw polls held by the Security Council to encourage a thinning of the field and to help to settle on a single candidate.
In every ballot, the 15 Security Council members assessed each candidate by voting either "encourage," "discourage" or "no opinion."
In the latest vote, Guterres received 13 "encourage" votes, no "discourage" votes and two votes of "no opinion."
The next closest candidates, Vuk Jeremic of Serbia and Miroslav Lajcak of the Slovak Republic, each received seven "encourage" votes and six "discourage" votes, while Bulgaria's Irina Bokova received seven "encourage" votes and seven "discourage" votes.
Guterres, 67, will replace the incumbent secretary-general, South Korea's Ban Ki-moon, whose second five-year term ends on December 31.
While there is technically no limit to the number of terms a secretary-general may serve, none has held office for more than two terms.
Former Portuguese PM
Guterres, a trained engineer who worked as an assistant professor before entering politics in 1974, led his country from 1995 to 2002 as head of the Socialist Party.
From 2005 to 2015, he served as the United Nations High Commissioner for Refugees. He is credited with cutting costs at the agency during his tenure, as well as lifting its performance as it grappled with the migrant crisis.
A practicing Catholic, Guterres remarried after his first wife died of cancer, and has two children.
In Guterres' vision statement in applying for the position, he wrote of the challenges facing the world in terms of rising inequality, terrorism and organized crime, climate change and the proliferation of armed actors internationally.
He wrote that the UN was "uniquely placed to connect the dots to overcome these challenges," but that change and reform was needed.
"People in need of protection are not getting enough. The most vulnerable, such as women and children, are an absolute priority. We must make sure that when someone sees the Blue Flag, she or he can say: 'I am protected'."
Speaking to reporters in Lisbon, Portuguese President Marcelo Rebelo de Sousa said he had congratulated Guterres.
"It is great for the United Nations because the best one was elected, and we many times have the feeling internationally that because of imbalances, weights and counterweights, not always the best is chosen. Here the best one was chosen," he said.
"This is very good for the world, very good for the United Nations, and it is very good for Portugal."
US, UK ambassadors praise choice
The ambassadors to the UN for the US and the UK -- both veto-wielding permanent members of the Security Council, along with Russia, China and France -- welcomed the result.
Samantha Power, US ambassador to the UN, said that "in the end there was just a candidate whose experience, vision and versatility across a range of areas proved compelling. People united around a person who has impressed throughout the process and has impressed across multiple axes in his service in Portuguese politics and at the helm of UNHCR."
Matthew Rycroft, the UK's ambassador to the UN, paid tribute to the seven women who had run for the role.
While it was "high time" for a woman secretary-general, he said, "it's fair to say that Antonio Guterres has come through this new and improved and more transparent process at the top of the league of the thirteen who competed."
He said the world needed a strong secretary-general who would "provide a convening power and a moral authority at a time when the world is divided on issues, above all like Syria."
"And I think that Antonio Guterres has demonstrated at the hearings and throughout this process that he is the person to do that."
Human Rights Watch welcomed the selection of Guterres, with the group's UN director, Louis Charbonneau, describing him as "an outspoken and effective advocate for refugees with the potential to strike a radically new tone on human rights at a time of great challenges."
Eastern European nations felt it was their turn
Guterres has long been the front-runner for the role.
Prior to Wednesday's vote, the candidate considered his closest potential rival was Bulgaria's Kristalina Georgieva, who only entered the race last month after that government said its other candidate, Bokova, had failed to win enough support in earlier straw polls.
Despite Guterres' clear lead, it was thought he could potentially face a veto from Russia, which had said it wanted a woman candidate, and would back an Eastern European nominee.
But Georgieva, currently serving as European Commissioner for Budget and Human Resources, ended up back in the field, with five "encourage" votes, eight "discourage" votes and two votes of "no opinion."
There was a strong sentiment among Eastern European nations that it was their region's turn to produce the next secretary-general, based on an informal notion of a rotation system -- although this is not provided for in the UN charter.
Many of the 13 candidates for the role hailed from Eastern Europe.