The airline, part of International Airlines Group (ICAG.L), will run the thrice-weekly flight from September 2013.
BA, which already flies to Beijing and Shanghai, also began services to South Korean capital Seoul earlier in December.
Chengdu, the prosperous capital of Sichuan province, is one of China's largest cities.
A long-running row over airport capacity expansion in Britain has centred on the need to improve links to major Chinese cities served by other European hubs such as Paris and Frankfurt. (Reporting By Christine Murray, Editing by Rosalba O'Brien)
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