"We've been a sponsor of the All Blacks and the New Zealand men's and women's sevens teams for the past 18 months.
"The Rugby Awards are the biggest night of celebration for New Zealand Rugby and it comes at the end of a long season, so being part of that celebration is a really attractive option for us," May said.
"It's another demonstration of our support for the sport in New Zealand."
Alcoholic beverage producers have long faced pressure to steer clear of advertising for sporting events.
In 2014 the Government was told to end alcohol sponsorship of sports clubs and ban any advertising of beer, wine and spirits during televised matches by a ministerial forum.
The forum, chaired by former rugby league coach and businessman Graham Lowe, concluded after a two-year inquiry that the total cost of alcohol-related harm in this country was "enough to justify further restrictions on alcohol advertising and sponsorship".
Lowe said yesterday that news of a new banking sponsor, as opposed to an alcohol one, was "fantastic".
"Steinlager has been a fantastic supporter of all manner of sport and has done a great job, but the scene is changing and I think the rugby union are leading the way."
Last year ASB took over the sponsorship of the former Tennis Open from beer producer Heineken.
The deal adds to ASB's existing sponsorship portfolio of the All Blacks, the All Blacks Sevens and the Black Ferns Sevens.
New Zealand Rugby chief executive Steve Tew said it was great to have ASB backing a key event in the rugby calendar.
"This is a night where the rugby community comes together to celebrate those who've made a difference in the game so it's fitting that a high performer and proud rugby supporter like ASB is backing this great event."
The annual awards evening will now be known as the ASB Rugby Awards, formerly the Steinlager Rugby Awards.