The song was first recorded at the Warners Publishing Studio, New York in early 1969 with Morrison's producer at the time, Lewis Merenstein. It was then rerecorded in both the spring and summer sessions in the same year, before Morrison returned to the track in the September to November sessions at the A&R Recording Studios, 46th Street, New York, that resulted in the recording of most of the tracks that were released on Moondance.
"Come Running" is composed in the key of A major, with a chord progression of A-D-A-D-A-D-A-D-A-D-A-E-D, which changes at the coda to A-F#m-A-D-F#m-Bm-D-A. The song has a bright rock tempo in 4/4 time, which slows at the three bar coda.
Morrison described it as "a very light type of song. It's not too heavy. It's just a happy-go-lucky song. There are no messages or anything like that." Brian Hinton's interpretation of the song was more complex: "The imagery is just like that at the end of "Madame George", a train passing, wind and rain ... an image of implacable nature against which human life and death play out their little games. Van and his lover 'dream that it will never end' while knowing that of course it will. Even the injunction to 'put away all your walking shoes' has a temporary sound to it."
Biographer Clinton Heylin remarked that "the lower rung chart success of the "Come Running" 45 hardly accounts for the album's [Moondance] immediate acceptance by a whole new spectrum of young adult listeners." The single peaked at number 39 on the Billboard Hot 100 singles chart.