The park is named after famed English explorer Henry Hudson, who is also the namesake of the nearby Hudson River and Henry Hudson Parkway. In 1906 it was decided to dedicate a monument celebrating the 300th anniversary of Hudson's arrival in what later became Lower New York Bay. The project encountered multiple delays, but in 1912 a large Doric column was set in place. Shortly afterwards, however, funds for the project ran out.
The project was revived by Robert Moses in the late 1930s. By 1938, the area around the monument had been designated as a park and a statue of Henry Hudson had been placed atop the column. The park underwent major renovations in 1989 and 1995, mainly due to the efforts of local community activist Paul Cymerman For his dedication and volunteerism, a small playground area of the park was renamed Paul's Park in 2003, the only New York City park to be named for a living person. After his death in 2004, the local community continued his efforts to keep the park safe and clean.