Eriksson, who during a long career most notably became the first foreigner to coach England, died in late August at the age of 76 after a battle with pancreatic cancer.
The Swede, who guided England to World Cup quarter-finals in 2002 and 2006, announced in February 2023 he was stepping back from public life due to "health issues".
His funeral service at the Fryksande church in Torsby in the western region of Varmland where the internationally renowned coach grew up began at 10:00 am (0800 GMT) on Friday.
A giant screen and benches were set up outside the church, showing the funeral live for local residents and other fans.
Among the 600 guests present inside the church were Beckham, who was a pivotal figure in Eriksson's England team, and another former England boss Roy Hodgson, Eriksson's family and his former partner Nancy Dell'Olio.
"Despite his illness, Sven-Goran's last days were full of life. He received tributes from all over the world. Many of you carry his commitment as a coach in your hearts," pastor Ingela Alvskog said in her eulogy.
"So much joy, so much laughter. In the midst of grief, there is room for gratitude," she continued.
Outside the church, several hundred people gathered, some dressed in their Sunday best while carrying roses in their hands.
"Sven-Goran loved routine and discipline. But he was also a great bon vivant who enjoyed good food, drink and travelling in first-class," added the pastor, who was close to "Svennis" -- as he is commonly called in Sweden -- and his family.
Eriksson had requested that the ceremony be a joyful event and should include New Orleans jazz.
In the autumn of his life, Eriksson, born on 5 February 1948 in Sunne, could already see time slipping away.
Eriksson wrote in a column for newspaper The Telegraph that was published after his death that his life as football manager had "been a dream."
"Do not give up, is my message for life. And please don’t forget this: life is always, always to be celebrated," Eriksson wrote.
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