"Celebration" has been described as a sleek dance-oriented track with influences of previous dance singles by Madonna from the early 90s such as, "Vogue" (1990) and "Deeper and Deeper" (1992). It constitutes of a pumping, house style music in it. "Celebration" is set in the time signature of common time with a dance beat tempo of 126 beats per minute. The song is set in the key of B minor with Madonna's voice spanning from F♯3 to B4. The song has a basic sequence of Em–F♯m–Bm–Bm as its basic chord progression.
Todd Martens from the Los Angeles Times stated that "Celebration" works as a throwaway, midsummer dance pop number. However, he felt that the song had modest goals, "at least by Madonna's standards. Even when it gets a bit risque, silliness rules the day. She invites us 'to the dance of life,' and coasts over the chorus." He went on to add that the song "is an effective look back, a gliding, reassuring number that Madonna hasn't forgotten her beginning. But rather than instill a sense of nostalgia, everything feels a bit obligatory. The sound of an artist, hopefully, ready for the next chapter."