Constitution Plaza came into being in the early 1960's as part of an urban renewal project. It replaced twelve acres of land that had historically been populated by newly-arrived immigrants in the city. At the time the project was proposed, the area was known as East Side, the Front Street/Market Street Italian district. The demolition of the area forced 108 businesses, 187 families and 31 individuals out of the neighborhood and was legally challenged in a case that went to the state Supreme Court in 1954. When the development concept won out, then-Mayor James H. Kinsella threw a brick through the window of a run-down building, marking the razing of the Front Street neighborhood.

The plaza takes its name from the nation's first written constitution that was drawn up in Hartford in 1639.

Largely comprised of office buildings, the plaza itself hosts a water fountain created by Masao Kimoshita that was designed with the awareness that a traditional fountain would likely soak passing pedestrians with spraying water due to frequent wind gusts across the plaza. In response to this, the fountain was designed to resemble a mountain stream, with water flowing downward in a gentle cascade. The fountain pool is paved with black stones from Japan, and slabs of Quebec granite and Georgia white marble comprise the horizontal and vertical slabs that create the sculpture through which was flows.

The clock tower, at the north end of the plaza, was also designed by Masao Kimoshita.

Much of the activity on the plaza is seen during the noon hour on weekdays during warm weather when workers flock to the plaza to enjoy the open space. Several festivals and events take place on the plaza, including the annual Festival of Light when the entire plaza comes alive during the December holidays.

More recently, with the connection of Constitution Plaza to Hartford's Riverfront Plaza, river views, noon-hour concerts and special events are more abundant. Still, Constitution Plaza is seen as under-utilized urban space.