Ray Dolby - who set the firm up after getting a physics PhD from Cambridge University - still owns a 70% stake, now worth more than $1.7bn.
Dolby invented a way of cutting background hiss in tape recordings and later brought out "surround sound".
From Clapham to California
The surround-sound system has been used in thousands of films, DVDs and video games.
Strong demand for home cinema and DVD systems have helped boost company profits, and Dolby reported net income of $39.8m on sales of $289m in the 12 months to the end of 24 September.
Analysts warned that earnings growth is unlikely to continue at its current pace as the home cinema market becomes saturated.
The company has said it is to focus on increasing revenues by licensing its technology to digital broadcasters and broadband internet providers.
Demand from investors was strong and the $18 price tag was up from the initial offer price of between $13.50 and $15.50.
The company, which was founded in 1965, had its headquarters on London's Clapham Road before it moved to California in 1976.
Its first noise reduction product was called Dolby A.
In 1975, the company released its stereo cinema system, refining it for home use in 1982.