The move is expected to lead to a double by-election in Leith Walk ward, which she has represented for the past eight years and where the SNP’s Deidre Brock is also standing down following her election as an MP.
Ms Chapman, who is co-leader of the Scottish Greens with Patrick Harvie, was selected as the party’s lead candidate on the North East regional list for next year’s Scottish Parliament elections.
But she has come under fire from within the party over her alleged lack of connections with the area – which stretches from Dundee to Aberdeen. And a petition calling for her to be deselected has been signed by leading Greens in the North East, including the former Green MSP for the region, Shiona Baird.
Ms Chapman dismissed the criticisms, saying she had been the “runaway winner” in a ballot of all party members in the region.
She said: “I was asked to stand by several members in the North East, I offered myself as a candidate and I was voted top of the list in April.
“There will always be people disappointed they didn’t get the position on the list they wanted.
“I have been working with groups in both Aberdeen and Dundee for years.”
Ms Chapman was elected Rector of Aberdeen University last year.
And she said she had recently got a new job in Dundee, with the Muslim Women’s Resource Centre, and would be moving there soon.
She said it “made sense” for her to shift her focus to the North East and with Ms Brock’s resignation, it seemed the right time to step down.
She said: “If I were elected to Holyrood in May I would have to stand down then, so it saves a second by-election and with proportional representation, having two seats to fill gives voters a chance to choose the representation they want.”
Ms Chapman said she believed the Greens had a good chance of getting list MSPs elected in most of the regions, fighting on a platform against austerity and in favour of economic and social justice.
She said it had been “a huge honour and privilege” to serve and work with the people of Leith Walk for the past eight years.
She said her proudest achievement on the council was Leith Decides, an initiative to give local people the power to decide on the allocation of community grants.
She was also convener of the petitions committee, which she said helped open up the council and let people feel they were being listened to.
Green group leader Steve Burgess paid tribute to Ms Chapman. He said: “I thank Maggie for her work as a Green councillor over the last eight years. We will campaign hard to ensure a new Green councillor is elected on a promise that only the Greens can offer a progressive and constructive opposition to the current Labour-SNP administration.”
A by-election to fill Ms Brock’s seat has already been fixed for September 10.