The 25-year-old scored six times in 43 appearances for the Tulips last season as they made it all the way to the Pitching In NPL Midlands Division play-off final.
Spalding were beaten in heart-breaking fashion by Halesowen Town in that match, letting in a stoppage-time equaliser before conceding again in extra-time.
Broccoli was on the books of Newcastle United in his younger days, before spending a number of seasons in the Italian lower leagues.
Robbie Nightingale has now moved to bring in the talented midfielder as Cambridge look to improve upon last season's 14th-placed league finish.
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