Yeang, who is famous for his green skyscrapers and ecological design approach, is expected to make the shock move to the practice within the next few weeks.
It is understood contract negotiations are already at a very advanced stage and Llewelyn Davies chiefs are hopeful Yeang will soon put pen to paper.
With both parties keen to keep the deal top secret for at least another month, most of the details still remain firmly under wraps and it is unclear whether the deal will lead to a name change.
However, there is widespread speculation the practice could come under a new banner, with the combined title of Llewelyn Davies Yeang currently being mooted.
The future of the 70 staff working at the T R Hamzah & Yeang office in Malaysia is also uncertain. At the time of going to press there were doubts about whether they had been formally informed of the deal.
Even so a source very close to the negotiations said 'there is no reason for them to worry for their jobs'.
Despite the veil of silence over the contract talks, it is no secret that Llewelyn Davies' principal director Stephen Featherstone has long been an admirer of Yeang's talents.
Back in February, Featherstone hailed the Malaysian-born designer as one of his biggest architectural influences (AJ 03/02/2005).
Yeang has had a long term association with the firm dating back decades and has already worked in collaboration with Llewelyn Davies on the Essex Design Initiative.
It is understood the practice is also working with Yeang on a number of 'green schemes' - the first of which could be unveiled before end of the year.
Born in Penang, Malaysia in 1948, Yeang has taught at the University of Sheffield since 1994.