To stay at 80 per cent of the adult minimum wage, the starting-out and training wages will increase from $13.20 to $14.16 per hour in April next year.
Lees-Galloway also laid out the likely increases in coming years, subject to economic conditions, to provide businesses and workers with greater certainty.
He said the minimum wage will rise to $18.90 an hour in April 2020 and $20 in April 2021.
National Party leader Simon Bridges said the increase was "too far, too fast", and small businesses would feel the pinch and possibly pass the extra costs to consumers.
"There will be people out there, workers who say 'fantastic', but it will have an effect either in some job losses or real cost of living increases," Bridges said.
Act Party leader David Seymour adding that New Zealand already had the highest minimum wage in the OECD, relative to the average wage of $31.34 an hour.
"Increasing it further shows a callous disregard for the impact it will have on small businesses."
Advice from Ministry of Business, Innovation and Employment is that a minimum wage of $17.70 would mean that 8000 fewer people in work, and Seymour said that could be "a cruel blow to young, unskilled workers looking for employment".
But Lees-Galloway said that the MBIE advice, even allowing for fewer new jobs, still estimated about 49,000 new jobs would be created next year.
With unemployment currently at 3.9 per cent, he said the issue was not the quantity of available jobs, but their quality and the amount of pay they offered.
The Government lifted the rate to $16.50 an hour in April this year, despite advice from MBIE that it could cost up to 3000 jobs.
A regulatory impact statement from MBIE officials said the higher cost of labour could be passed on to consumers through higher prices for goods and services, but also noted that the effect on employment "is heavily debated in economic literature".
"There is no clear consensus".
The living wage - reflecting basic expenses such as the cost of food, transportation, housing and childcare - for 2018 is $20.55 per hour, as calculated independently by the NZ Family Centre Social Policy Unit.
The boost comes as economists warn of a tight labour market.
According to the latest figures from the Half Yearly Economic and Fiscal Update, GDP growth was expected to be roughly 3 per cent over the next five years.
Minimum wage increases:
• April 2019 - $17.70
• April 2018 - $16.50
• April 2017 - $15.75
• April 2016 - $15.25
• April 2015 - $14.75
• April 2014 - $14.25
• April 2013 - $13.75
• April 2012 - $13.50
• April 2011 - $13.00
• April 2010 - $12.75
• April 2009 - $12.50
• April 2008 - $12.00