Hookway spent 35 years at oil major BP PLC (LON:BP) in various roles, including heading up the finances of the BP's downstream business and more recently as chief operations officer of BP's Global Business Services & IT unit.
Hookway replaces Mark Hanafin, who is due to retire in March 2019. Hanafin's retirement was announced in July.
Centrica said Hookway would join its board on December 1, when he will also start his new role.
"I am delighted Richard is joining Centrica as chief executive of Centrica Business. He brings with him a wealth of experience in customer-facing energy activities, including in energy marketing and trading and commodity risk management. He has spent much of his career in the UK and Europe, but has also lived in North America and knows that energy market well," Centrica Chief Executive Iain Conn said in a statement.
Centrica shares were down 0.4% at 143.80p in late morning trade.