Cooper made the call on Sixth Avenue in New York, before going into a press conference using a Motorola DynaTAC -- a device that weighed one kilogram, (2.2 pounds) and had a battery life of 20 minutes, according to Motorola.
Cooper told the technology website The Verge last year that he placed the first call to a rival, Joel Engler of Bell Labs.
"To this day, he resents what Motorola did in those days," Cooper said.
"They thought that we were a gnat, an obstacle... we believed in competition and lots of players. And we also believed -- our religion was portables, because people are mobile. And here they were trying to make a car telephone and a monopoly on top of that. So that battle was the reason that we built that phone."
Cooper and his team were honored earlier this year with the Draper Prize by the National Academy of Engineering for their work.
In 40 years, the industry has come a long way. Research firm IDC predicts 900 million smartphones will be sold in 2013 -- along with roughly the same number of more basic feature phones.
And the phone has become a key advertising platform -- eMarketer said US mobile advertising spending grew 178 percent last year to $4.11 billion, and spending is expected to rise a further 77.3 percent to $7.29 billion in 2013.