Eriksson's wooden coffin was covered in white flowers and surrounded by six tall candles and other floral wreaths as the ceremony began inside the 600-seat Fryksande church.
"It is a day of grief but also a day of thankfulness," the priest, Ingela Älvskog, told those in attendance.
Beckham, who arrived by private jet on Thursday, greeted Eriksson's 95-year-old father Sven and other family members with hugs inside the church before the funeral started.
Eriksson became England's first foreign-born coach when he led the national team from 2001-06, and made Beckham his captain.
Eriksson, who also won trophies at club level in Italy, Portugal and Sweden, died on Aug. 26 at the age of 76, eight months after he revealed he had been diagnosed with pancreatic cancer and had at most one year to live.
Some 200 seats in the neo-Gothic church from 1898 were reserved for his family, friends and players from his career in the football world, according to his agent. The remaining seats were open for the public, according to Eriksson's wish, with a big screen set up outside the church where hundreds more gathered to watch the ceremony. The funeral was also broadcast live on some Swedish media websites.
The wooden coffin was wheeled in by pallbearers at the church Friday morning as fog wrapped Torsby — a town of about 4,000 people located about 310 kilometers (193 miles) west of Stockholm. Next to the casket was a photo of Eriksson on a small table. The floral wreaths included ones sent by FIFA and Lazio, the Italian team that Eriksson led to the Serie A title in 2000.
The ceremony began with somber piano and organ music, but later took on a more upbeat note with Swedish singer Charlotta Birgersson performing Elton John's song "Candle In The Wind" and then "My Way" in a duet with Johan Birgersson, who later intoned the popular Italian song "Volare" after the family had gathered around the casket to lay flowers.
Beckham also visited Eriksson in Sweden in June to say goodbye. Others attending the funeral included the Swedish coach's longtime partner Nancy Dell'Olio. Eriksson's agent had said that guests from England, Italy and Spain were expected.
After the funeral, the casket was carried out of the church by eight men to the hearse. The guests then walked in a procession accompanying the coffin to a nearby museum where speeches and eulogies to the coach fondly known as "Svennis" were planned on an outdoor stage. A brass band played during the procession through Torsby, including the tune "You never walk alone" from the musical "Carousel" which has become the anthem of Liverpool, the club Eriksson supported since childhood.
The local soccer club Torsby IF, where Eriksson started his career in the 1960s, wrote on its webpage that "you also showed your greatness by always being yourself, the caring Svennis who talked to everyone and took the time, for big and small, asking how things were and how the football was going. We will miss you."