The move will be a severe blow for the firm, as Hyams had headed up its 'creative studio' for the last two years.
Hyams described his departure as 'tragic', claiming 'great progress' had been made since he took the studio on.
Hyams ( second right) had been something of a rising star at Foster and Partners before being poached to improve design standards at Aedas.
It was seen as a significant move by the practice - ranked second in the AJ100 with 190 architects - to improve its design reputation.
The reasons behind Hyams' decision to resign remain unclear, but one source has speculated that there may have been some disagreement about the autonomy enjoyed by the studio.
'I joined to set up the studio and it was widely believed to be very successful as a catalyst for change in the rest of the practice,' Hyams told the AJ.
'So much so that CABE said they were monitoring it to see how successful it was.
'This is tragic, though, because as a way of increasing standards in commercial practices it was a great idea,' he added. 'We were commissioned to up the ante in the rest of the practice - and we did.'
In an official statement, Aedas said existing director Brian Johnson would take over the studio and it would become a 'creative team' that would spread throughout the practice.
Hyams said he was yet to decide what to do next, but that he wasn't ready 'to fall in love again for a while'.