The role is currently filled by former HSBC chairman Lord Green, who will stand down at the end of the year, the Prime Minister told the Commons.
Mr Cameron told MPs Mr Livingston would "bring huge talent to a vital national effort".
At Prime Minister's Questions Mr Cameron said: "At the end of the year Stephen Green, the former chair and chief executive of HSBC will be standing down as trade minister after doing a superb job refocusing the Government's efforts in key export markets.
"I can announce today that Ian Livingston, for the past five years chief executive of BT, one of Britain's most successful businesses, will take on this vital role. I believe he will bring huge talent to a vital national effort."
Mr Livingston, who will be made a peer in order to take up his ministerial role, said: "I am honoured to have been asked by the Prime Minister to take on the role of Minister for Trade and Investment, with a remit of helping the growth of British companies and the country's future economic success.
"I am immensely proud to have led this company over the last five years. We have made huge progress over the last few years but I know there is still so much more that BT can and will do."
Gavin Patterson will take over as chief executive of BT Group in September, the firm announced.
Mr Patterson has served as chief executive of BT Retail and as a BT board member since 2008, having joined the company as a senior executive four years prior to that.