Benita Mehra tendered her resignation to the Prime Minister Boris Johnson, saying she recognised and respected the "depth of feeling" among some about her appointment.
Mr Johnson thanked Ms Mehra for her commitment and said he was "grateful for her sensitivity to the work of the inquiry".
Her resignation was welcomed by the bereaved families and survivors group Grenfell United – which had raised concerns about the link with the Arconic Foundation.
They said Ms Mehra had "done the dignified thing by resigning", but said the Government "should never have put families in this situation".
It was announced shortly before Christmas that the engineer would replace academic Professor Nabeel Hamdi on the panel for the second phase of the inquiry, which is due to begin this year.
It was later disclosed that Ms Mehra is an immediate past president of the Women’s Engineering Society (WES) which, according to the society’s website, last year received funding from Arconic for an apprentice conference.
Arconic supplied the cladding on the outside of the west London tower block, which went up in flames on June 14 2017, claiming 72 lives.
Vice-chair of Grenfell United, Karim Mussilhy told ITV News: "We think Benita has done the right thing, so it is good that she has resigned."
He added: "Frustrated though that it has taken so long to do this.
"It is Saturday night and the inquiry starts on Monday and everything was really up in the air up until her resignation letter but the Government still have a lot of questions that they need to answer."
A report following the first phase of the inquiry concluded in October last year that the cladding did not comply with building regulations and was the "principal" reason for the fire’s rapid and "profoundly shocking" spread.
Arconic said a "confluence of unfortunate circumstances" rather than the “mere presence” of the panels had caused the spread of the fire.
In a letter to the PM, Ms Mehra said: "As you know, I had hoped to draw on my experience and knowledge of the construction industry, of community engagement and of governance within housing management to contribute to the vital work of the inquiry in discovering how and why the devastating fire at Grenfell Tower happened.
"However, it is apparent that my former role as President of the Women’s Engineering Society (WES), which in 2017 accepted a charitable donation from the Arconic Charitable Foundation to support the mentoring of women engineers, has caused serious concern to a number of the bereaved, survivors and resident Core Participants."
She said her role at the WES was unpaid and the grant from Arconic was ringfenced to fund the mentoring scheme.
"For these reasons, I did not link any aspect of my former role as President of the WES to my panel member role for the Grenfell Tower inquiry.
"In hindsight, this was a regrettable oversight on my part.
"I am confident that had I continued in my role at the inquiry I would have approached my work with complete independence and impartiality at all times.
"However, I recognise and respect the depth of feeling among some Core Participants about my appointment."
Boris Johnson said: "I can confirm that Benita Mehra wrote to me yesterday to offer her resignation from the Grenfell Tower Inquiry panel and I have accepted.
"I would like to thank Benita for her commitment and I am very grateful for her sensitivity to the work of the inquiry.
"As the inquiry’s phase 2 hearings begin, we remain completely committed to getting to the truth of what happened, learning lessons and delivering justice for the victims."