Crown replaces Greg Dyke, who had held the job since the start of 2006, after he was appointed independent Football Association chairman.
Crown told the club's official website: "I am honoured to have been appointed chairman of Brentford and look forward to working with the board and the management team to build on the progress made over the last two years and to deliver a successful future for the club and its fans.
"I hope to continue the great work of Greg Dyke, who played such an important role in getting the club to where it is now."
The Bees have also appointed Donald Kerr and former chairman Eddie Rogers as vice-chairmen.
- Sports & Recreation
- Greg Dyke