At least two students every year will be given the chance to study architecture under the scheme.
Stephen, who was only 18 when he was killed by racist thugs at a bus stop in Eltham, South London, five years ago, wanted to become an architect.
A friend of the Lawrence family said: "There's a huge amount of goodwill around at the moment and it's important to channel that into something positive. The educational trust will be a long-lasting way of keeping Stephen's memory alive."
Stephen's parents, Neville and Doreen Lawrence, and representatives of the Lawrence Family Campaign met on Tuesday to discuss how the trust would be administered. It is expected to make annual grants to two aspiring architects - one from Britain and one from Jamaica - the Lawrence family's country of origin.
The trust will have an official launch at London's Jamaican High Commission in September.
Initially the trust will run on public donations which have flooded in since Stephen's parents began their legal fight to bring his killers to justice. It is hoped that it will be given charitable status, securing its long-term future.
Stephen was studying for three A-levels at the time of his murder. He had been impressive enough on a work placement with a local architect to secure a job offer.
The public inquiry into the Metropolitan police's handling of Stephen's death, which has heard allegations of police racism and corruption, ended its first phase 10 days ago, to allow inquiry chairman Sir William McPherson time to assess the evidence of 88 witnesses.
The inquiry will recommence in September. Sir William's full report is expected early next year.