The comments led to accusations of transphobia, which the artist denied.
In a statement on Wednesday morning, the Royal Academy said: “There has been a great deal of debate around the RA’s recent communication about no longer stocking the work of Jess de Wahls in the Royal Academy shop. We have thought long and hard since then about this and the wider issues it raises.
“One thing is clear to us now - we should have handled this better. We have apologised to Jess de Wahls for the way we have treated her and do so again publicly now. We had no right to judge her views on our social media. This betrayed our most important core value - the protection of free speech.
“There was also a failure of communications internally which resulted in Jess de Wahls first hearing via social media that we would no longer stock her product in the RA shop. We will now reopen discussions with her regarding the restocking of her work.”
The statement added: “We will continue to reflect on this and to look at our internal processes to ensure we learn from it. We want to make sure we navigate this better in future”.
The artist had said she would consider legal action if she did not receive an apology.
The academy had been accused of breaching the Equality Act by removing from sale the embroidered flowers by Ms de Wahls.