The World Food Programme had halted distributions in Huthi-controlled territory in June following accusations of "diversion of food" meant for Yemeni civilians.
But in a deal signed last week, the Huthis offered guarantees concerning the beneficiaries of aid, the UN agency said.
"WFP will resume food distributions following the Eid Al Adha festival for the 850,000 people in Sanaa City who have not received food rations from WFP for the last two months," WFP spokesman Herve Verhoosel told reporters in Geneva.
The Eid festival begins on Sunday and continues to Wednesday.
Verhoosel added that WFP is also starting the roll-out of a biometric registration system targeting nine million people, which will help identify legitimate beneficiaries of food aid in Huthi-held areas.
The UN has repeatedly described Yemen as the world's worst humanitarian crisis, where 24.1 million people, some 80 percent of the population, is in need of aid.
Fighting between the Iran-backed Huthis and government forces aided by a Saudi-led coalition has killed tens of thousands of people, most of them civilians, aid agencies say.