Hogg, a former business and city editor at The Independent, will replace outgoing non-executive chairman of 3i, Sir George Russell, when he retires in December.
Hogg already holds directorships at automotive engineering group GKN and cruise ship operator P&O Princess Cruises. In addition, she is a member of the House of Lords select committee on economic affairs.
She had been tipped as a possible candidate to succeed Sir Christopher Bland as chairman of the BBC when he leaves to join ailing telecoms firm BT. The current frontrunner for the position is Goldman Sachs economist and BBC governor Gavin Davis.
Hogg is going to review her current responsibilities in view of her new appointment.