Professional speech writers?

Roughly 100 years. Judson Welliver is the first person specifically hired to write speeches for an American president- for Warren Harding in 1921 and continued to work for the POTUS into Coolidge's term, though his official title was 'literary clerk'. That doesn't mean previous presidents didn't have their speeches ghost written or at the very least beefed up a bit, though- Hamilton very likely at least assisted George Washington punch up his oration if not entirely write it himself on occasion, so there have been people helping the man in office since the beginning.

However, Welliver was definitely the first to do so professionally, and the society for former Presidental speechwriters is named after him: The Judson Welliver Society. And, of course, in the true fashion of someone you'd expect to hold the position, he went on to greater things after leaving that job: he became a PR man for oil.

As for FDR: he did also use ghost writers, though not exclusively and not without his own revision. His "Day of Infamy" speech, for instance was entirely penned by him, but other speeches were not. Perhaps most notable was Harry Hopkins, one of FDR's closest advisers, who also wrote his third inaugural speech- a man rarely talked about but utterly vital to Roosevelt's administration and both his New Deal efforts and his diplomatic efforts in WW2.