Rundgren was born in Upper Darby, Pennsylvania, the son of Ruth (née Fleck; April 29, 1922 – April 6, 2016) and Harry W. Rundgren (1917–1996). He grew up in Upper Darby. His father was of half Swedish and half Austrian descent, and his mother was mostly of German descent.
Todd was a 1966 graduate of Upper Darby High School. During high school, he ran an underground newspaper that mocked his teachers and was frequently suspended for growing his hair long. After graduation, he moved to Philadelphia and began his career in Woody's Truck Stop, a blues rock group in the style of Paul Butterfield Blues Band. However, Rundgren and bassist Carson Van Osten left prior to Woody's Truck Stop releasing its eponymous first album to form the garage rock group Nazz in 1967 with Thom Mooney (drums) and Robert "Stewkey" Antoni (vocals and keyboards). The group gained minor recognition with the Rundgren-penned songs "Open My Eyes" and "Hello It's Me". (He later recorded a solo, uptempo version of "Hello It's Me"; it became one of his signature songs.)
Nazz released three albums during this time – Nazz (1968), Nazz Nazz (1969), and Nazz III (1971). "Open My Eyes" gained belated recognition thanks to its inclusion in Nuggets (1972), the genre-defining anthology of American 1960s garage punk and psychedelia compiled by musician Lenny Kaye. The group's second LP was originally intended as double album (titled Fungo Bat), but instead a truncated version was released as Nazz Nazz in April 1969. Rundgren and Van Osten left the band shortly after. Under Stewkey's leadership the band continued (with new members) until 1970, and their label released a third LP Nazz III, on which most of Rundgren's vocals on the unreleased songs from the Fungo Bat sessions were replaced by Stewkey's.
Rundgren's distinctive style was inspired by a wide variety of musical influences—British pop-rock & baroque pop (notably Pink Floyd, The Beatles, The Who, The Yardbirds, Cream and The Move), the intricate vocal harmonies of The Beach Boys, classic American rock and roll, Broadway musicals, the operettas of Gilbert & Sullivan and American soul and R&B, but as his music evolved he demonstrated an increasing interest in other genres as well, such as hard rock.
Particularly during the early years of his career, Rundgren's songwriting was heavily influenced by the music of singer-songwriter Laura Nyro:
- "I knew her fairly well. I met her right after Eli and the Thirteenth Confession. I actually had arranged a meeting, just because I was so infatuated with her and I wanted to meet the person who had produced all this music. We got along, and we were kind of friendly, and actually, after I met her the first time, she asked me if I wanted to be her band leader. But the Nazz had just signed a record contract and I couldn't skip out on the band, even though it was incredibly tempting."
Rundgren's debut solo album Runt (1970) includes the strongly Nyro-influenced "Baby Let's Swing", which was written about her and mentions her by name.
Nazz manager Michael Friedman, who had joined Albert Grossman management brought Rundgren to the firm where he became both a solo artist and producer for many artists in the Grossman stable.