Farmers have also been quick to back the deal which will now charge backpackers 19 cents from the first dollar they earn from the start of next year.
The government under former prime minister Tony Abbott had originally planned to make people on working holiday visas pay 32.5 cents in the dollar, rather than enjoying a tax-free status.
"I would say that when you do the work and you consult properly, you come to the right outcome," Mr Morrison told reporters in Canberra after getting backing from the cabinet on Tuesday.
Backpackers are a vital supply of workers for the agricultural sector, with as much as a quarter of the industry's workforce in Australia on a working holiday visa.
The treasurer insists the changes will put working holiday makers in Australia on the same footing as if they were in Canada, New Zealand and the UK.
Nationals leader Barnaby Joyce said the compromise was a win for farmers.
The National Farmers Federation said the agricultural community feared its temporary workforce would be decimated by a clear disincentive for backpackers to come to Australia.
"The NFF has always advocated for a rate of 19 per cent as a fair and reasonable measure," president Brent Finlay said.
But Opposition Leader Bill Shorten described the backpacker tax as a "mess from day one" and its botched handling typical of the Turnbull government.
"They make a poor decision, poorly execute it, they then refuse to back down until they are kicking and screaming, then they come up with a new policy that's made on the run," he said in Brisbane.
Mr Shorten wouldn't commit to backing any of the proposed measures in the package, even though Labor banked the revenue from the initial proposal in its election costings.
Under the plan, working holiday makers will be taxed 19 per cent on any earnings up to $37,000, starting from January 1, 2017.
Earnings above that will be taxed at the same marginal tax rates as everyone else.
There will also be a $50 cut to the working holiday visa application fee to $390.
The government will spend $10 million promoting Australia as a destination for backpackers after many in the tourism and agriculture industries were concerned the original tax changes had deterred young people from coming to Australia.
To pay for this, working backpackers will be charged 95 per cent tax on superannuation payments once the working holiday maker leaves Australia.
It will also hike departure taxes by $5, to $60, in the first increase to that charge since 2012.
Tourism groups supported the reduced tax on working holiday makers, but criticised the increase in the passenger movement charge as "counter-productive".
