Law, who had taken over the chief executive reins after Abraham left to join Discovery Networks Europe last April, returns to the role of chairman, with Henderson and Teer now relieving him of day-to-day agency management.
Henderson joined St Luke's from Bartle Bogle Hegarty in 1996, and will continue to head the agency's BT account. He was one of three senior account directors promoted to the position of managing partner in November 2000.
Teer, a founding member of St Luke's, joined in 1995 from Abbott Mead Vickers BBDO, but has a relatively low profile in the industry. His promotion may surprise observers because he was not one of the agency's three managing partners.
The agency has endured a tempestuous 12 months, losing key accounts such as HSBC and Ikea, but has since won new business from Emirates, AMP and BT.
Law said: "Phil and Neil are steeped in the experimental creative culture of St Luke's, yet they have ambitious plans of their own. They are the perfect candidates for a unique and important job that would otherwise be impossible to fill."
Teer said: "The fact that a planner has become managing director signals that this is a very strategic job."
Henderson added: "We've fundamentally changed the way an agency operates and our string of new business wins demonstrates how attractive this is right now."