Answer by taking a quote from the following article:

Pinky and the Brain is an American animated television series. It was the first animated television series to be presented in Dolby Surround and the fourth collaboration of Steven Spielberg with his production company, Amblin Television, and produced by Warner Bros. Animation. The characters first appeared in 1993 as a recurring segment on Animaniacs. It was later picked up as a series due to its popularity, with 65 episodes produced.

As with Animaniacs, Pinky and the Brain was scored by a team of talented composers, led by Emmy-Award-winning composer Richard Stone. This team included Steven Bernstein and Julie Bernstein, who also orchestrated and sometimes conducted the 40-piece orchestra. The recordings were done on Stage A on the Warner Bros lot, the same stage (and with the same piano) where Carl Stalling recorded his Looney Tunes music. The theme music for Pinky and the Brain was composed by Richard Stone with lyrics by Tom Ruegger.  Two versions of the opening sequence and theme, with slightly different lyrics, were used during Animaniacs shorts. In the first version, Yakko, Wakko, and Dot (voiced respectively by Paulsen, Harnell, and MacNeille) popped up in the lab and sang the theme while letting the two mice out of their cage. The second, later version had the singers off-camera as the Brain picked the lock on the cage door with a small needle to free himself and Pinky. On the Pinky and the Brain show, the theme gained an additional two verses and was sung by Harnell, Dorian Harewood, Jim Cummings, and Paulsen.  The score sometimes includes references to classical music. For example, in the episode where the Brain builds a new Papier-mache Earth, the theme from the 2nd and 4th movements of Dvorak's 'New World Symphony' can be heard throughout the episode. The episode Napoleon Brainaparte makes frequent reference to the French anthem, La Marseillaise, while in the episode in which Pinky becomes the artist "Pinkasso" Mussorgsky's Pictures at an Exhibition can be heard.

Who made the music for Pinky and the Brain?
scored by a team of talented composers, led by Emmy-Award-winning composer Richard Stone.