The bridge opened to traffic on January 15, 1963, the same day that the Cross Bronx Expressway was completed.

[5] The bridge design included a set of spiraling ramps (officially known as the Highbridge Interchange and colloquially known as "The Corkscrew") to connect to and from the Major Deegan Expressway (completed in 1964) and a viaduct ramp connecting to Harlem River Drive, both of which are over 100 feet (30 m) below the level of the bridge, and access to Amsterdam Avenue.

[6] The Alexander Hamilton Bridge was planned in the mid-1950s to connect Robert Moses' proposed Trans-Manhattan and Cross-Bronx Expressways and to accommodate the additional traffic resulting from the addition of the six-lane lower level to the George Washington Bridge.

[5][7] With the Interstate designation, 90% of the $21 million in construction costs were covered by the federal government.

[9][10] While the traffic jams created from the construction had not been as bad as local officials had anticipated, inbound delays at the Hudson River crossings increased after the project began.