Beethoven was a transitional composer between the classical and romantic styles. There never really was a sudden change of styles. The classical form continued into the nineteenth century. Symphonies still had four movements, (generally), and there was still the developement sections etc, typical of the sonata or classical form.
Beethoven added a measure of dramatic feeling into his music, that was brought further by some of his successors like Schubert or Liszt.
The romantic period in arts started around the time that Beethoven was composing, but he was never strictly a romantic composer.