Davidson spoke out against what she called the fiscal and moral deficit left by the previous government.
James Shaw said Davidson's campaign energised and inspired the party's grassroots. "You lit a wildfire in the party."
Marama Davidson told reporters after the announcement of her co-leadership win that in campaigning for the job she had pledged to maintain regular, transparent communication with the party membership.
She said this didn't mean there would always be agreement. It was to create the space where members felt they were participating in the controversial issues facing the caucus.
Shaw reiterated it was an advantage in the party's first term in a governing arrangement to have a non-minister as co-leader to focus on communications with members.
"The risk is we don't take supporters with us."
The announcement in central Auckland today follows an election by party delegates. The Greens said 144 delegates cast their vote.
The election was needed because of the resignation of co-leader Metiria Turei before last year's parliamentary general election.
Davidson, of Maori ancestry and from the more activist wing of the party, styled herself as the natural heir to Turei, and was considered the frontrunner in the race for the female co-leadership.
She also emphasised her place outside the ministerial executive as giving her an edge in being able to differentiate the Greens from the Labour-led Government.
Genter too said she could differentiate the Greens from the Government, despite her being a minister outside cabinet and holding three portfolios.
The Minister for Women and Associate Minister of Health and of Transport, Genter campaigned on improving links between the Green caucus and the party membership.
She is seen as representing the urban liberal wing of the party, but she rejects this narrow categorisation, pointing to her activism in peace, environmental, social justice and other issues.
The co-leadership selection was made by electorate delegate vote. Every electorate was asked to select a delegate to cast a vote after discussions with their branch.