The laws lump together fast-tracked personal tax cuts with a handful of business tax breaks.
The legislation passed the upper house on Friday after the government put a time limit on debate.
Prime Minister Scott Morrison was in the chamber to observe the final series of votes.
The low income tax offset will now be lifted from $445 to $700.
The top threshold of the 19 per cent personal income tax bracket will increase from $37,000 to $45,000 backdated to July 1.
And the top threshold of the 32.5 per cent income tax bracket will rise from $90,000 to $120,000.
Adjustments will be made to ensure taxpayers have the correct amount of tax withheld from their pay going forward.
The low and middle-income tax offset will be retained for 2020/21 and received after individuals lodge their tax returns for the financial year.
Crossbench senators are furious Labor helped the government push its tax changes through.
Independent senator Rex Patrick admitted during debate that he was speaking from an uninformed position as he hadn’t been given enough time to scrutinise the hundreds of pages explaining the bill.
Senator Patrick put the blame on Labor for helping the coalition clear the laws.
“I’m thinking of assisting the Labor Party in its marketing. I’m going to go out and help you find a mascot,” he told the chamber.
“It’s going to be a dog and it’s going to be a dog that rolls over. It’s going to be one that rolls over the moment any member of the coalition comes into the room.”
Greens senators are dismayed the bill won’t be scrutinised by an upper house inquiry.
The minor party attempted to change the bill but its efforts were thwarted.
Greens senator Larissa Waters says the tax package will benefit higher income earners at the same time the government has cut JobSeeker and JobKeeper payments.
“This community deserves better,” she said.