Tucker was born in Boston, Massachusetts, the son of Maggie Moss, a public relations and marketing analyst and executive, and Paul Hayes Tucker, a curator, writer, and university professor who is an expert on Claude Monet and French Impressionism. Tucker's father is Irish American and Catholic and his mother is Jewish. He was raised in Boston's Irish neighborhood of Charlestown and attended the Park School in Brookline, Massachusetts. Tucker attended summer camp at Camp Chingachgook on Lake George in Pilot Knob, NY, part of the Adirondacks, during the 1990s.

Tucker attended the Boston Ballet and played 'Fritz' in their production of The Nutcracker when he was in third grade. He was also featured in a Boston Ballet calendar and attended the Thacher School in Ojai, California, graduating in 2001. He deferred from Columbia University, where he was accepted for early admission.