He will take up the position at start of next year, after current chief executive Sam Laidlaw retires from the board.
Conn is currently the head of refining and marketing at BP, and has been appointed by Centrica as regulators investigate the energy market.
“I am excited to be joining Centrica, a company which is leading the way in the provision of secure and reliable energy and services to customers in the UK and North America," he said.
"I recognise the challenges which we face in rebuilding customer trust in the sector and helping to create an effective and sustainable approach to energy markets."
His salary will be set at £925,000, but his bonus will depend on whether he hits performance targets. Centrica said that in April 2016 he could get a bonus in shares of up to the value of his salary.