The 74-year-old died on January 9 after suffering a stroke.
His career spanned more than 50 years and he was a regular Top of the Pops presenter in the 1970s, but was best known for children's TV show Crackerjack, which he hosted from 1973 to 1979.
He was one of the first presenters on Radio 1 when it was launched in 1967.
Celebrities attended including Mike Read, Carry On actress Anita Harris, Bobby Davro, John Virgo and DJ Adrian Juste.
The father of two, who had four grandchildren was celebrated at St Peter's Church in Bournemouth, Dorset.
Mark Carolan, the husband of Stewart's daughter Francesca, led the mourners with a rendition of the presenter's catchphrase: "It's Friday, it's five to five, it's Crackerjack!"
He said: "Simple words that many millions remember him by, but a select few remember him for so much more than that, how positive he was about everything in life."
Reading a eulogy from the family, Mr Carolan added: "You are a true legend, your legacy will live on, your passion and love now lives on through all your grandchildren."
His 10-year-old grand-daughter Kenza Carolan also paid tribute to Stewart and said: "He would make us laugh, life was an adventure every day."
Speaking after the service, his sister, Sue Mainwaring, said: "It was brilliant, I just can't believe how many people were there. It was such a shock he had that massive stroke.
"People would say he was very mean but he bought me my first horse, he's not mean. He loved being in the limelight, he was very loyal to his family."