The company, which earlier this year was forced to deny rumours of a boardroom split, said it would be appointing a non-executive chairman from outside the group in due course.
Sir David, 64, former chief executive of Vickers and currently deputy chairman of TSB, was coming up to the end of his contract.
"I feel that it is a good time for me to make way for a new chairman who is in a position to commit his time to Inchcape for several years to come," he said.
He admitted it had been a challenging time for the group, which has seen its shares fall after three profits warnings since the beginning of 1994. The strong Japanese yen has hit the company's car import business, which distributes Toyota and Mazda vehicles, along with a number of other models.
Last week Inchcape, the world's largest car distributor, said it was shedding 2,000 jobs in the Far East from its 48,000-strong workforce. About pounds 3bn of Inchcape's pounds 6bn in sales are with, or through, Japanese motor groups and the yen's strong rise over the past 18 months has taken its toll on profits. The shares have crashed from a peak of 565p to yesterday's close of 330.5p, up 2p.
Although Inchcape can see light at the end of the tunnel after the recent weakening of the Japanese currency, it failed to stem rumours of a rift - hotly denied - between Sir David and Charles Mackay, chief executive. Yesterday, Mr Mackay said: "Sir David has made a major contribution to the direction of Inchcape, helping to guide us through a difficult period in our history."
After leaving Vickers, Sir David was persuaded out of retirement to join Inchcape where, although technically a part-time chairman, he gained a reputation as a hands-on director. He will retire at the end of this year. A spokesman said the new non-executive would be very much a part- time post.
Inchcape shares have picked up recently, though brokers have reduced 1995 profit forecasts by about pounds 18m to pounds 165m to reflect restructuring costs.