Churkin was surrounded by ambassadors from the 14 other United Nations Security Council states as he made the announcement in New York on Wednesday.
Guterres came top of the Council's sixth closed-door poll of the 10 remaining candidates to replace current Secretary-General Ban Ki-moon.
"Today, after our sixth straw poll, we have a clear favorite and his name is Antonio Guterres," Churkin said.
During the informal vote, the former Portuguese prime minister received 13 "encourage" votes, no "discourage" votes and two "no opinion," one of whom was cast by a permanent Security Council member.
Wednesday's vote was the first to use colored ballots to distinguish the votes of the Council's five veto-wielding members.
A "discourage" vote from any of the permanent Council members - Russia, China, France, the UK and the US - could have severely damaged Guterres' prospects.
The 67-year-old Socialist politician also held the number-one spot in the previous five informal polls.
In a Tweet shortly after the announcement, US ambassador to the UN Samantha Power described the Council as "united" in its decision to recommend Guterres.
France and Britain also gave their approval, with the UK's envoy Matthew Rycroft saying Guterres would make a "very strong, effective secretary-general."
No final decision, yet
The Council will take a formal vote on Thursday and will then send its recommendation to the UN General Assembly, which will also take a vote to essentially rubber-stamp the council's decision.
Guterres' likely appointment comes despite a campaign by 50 nations to elect the first female UN chief.
The role is traditionally rotated among different regions of the world, leading to assumptions that it was now the turn of East Europe.
All 10 candidates faced two-hour interviews with members of the General Assembly, at which many diplomats said Guterres performed best.
As Portuguese leader, Guterres moved his Socialist party from the extreme left to the center ground, adopting business-friendly policies and undertaking a large privatization program. He also established a minimum income for families.
In his role as the head of the UN's refugee agency (UNHCR), Guterres campaigned hard to push wealthy countries to take in more migrants, fleeing conflict in Syria, Iraq and Afghanistan.
Ahead of last year's European migrant crisis, he warned that the continent would see an influx if it did not do more to help Syria's neighbors Turkey and Jordan to deal with the millions of refugees pouring over their borders.
Current UN chief Ban's second five-year term ends on December 31.
mm/msh (AFP, AP, Reuters)