The benchmark S&P/ASX200 index on Tuesday gained 113.4 points to 6976.9, a 1.65 per cent increase, while the broader All Ordinaries added 114.7 points, or 1.63 per cent, to 7169.5.
"So no one likes surprises and we got a hike that was in line with expectations, so the Aussie share market continued to rally," Saxo Markets analyst Jessica Amir said.
"We were already higher from the get-go and then we just extended on those gains after the RBA ticked that box and hiked rates in line with expectations, by 0.25 percentage points."
Ms Amir said a technical indicator known as the relative strength index (RSI) indicated the ASX200 was poised to extend its rally.
"We could potentially march up about 3.0 per cent to 7,140 and we'll pause and reflect," she told AAP.
But she cautioned the Federal Reserve could unwind these gains with a hawkish surprise at its next policy announcement early on Thursday, Australian time.
On Tuesday, all sectors were higher, with materials leading the way with a 2.6 per cent gain.
"For the most part, what is driving the market is commodities," Ms Amir said. "The US dollar has fallen over and most commodities are traded in US dollars."
BHP climbed 2.8 per cent to $38.42, Fortescue Metals rose 5.4 per cent to $15.50 and Rio TInto added 2.6 per cent to $90.49.
Nickel miners did well, with Nickel Industries climbing 7.5 per cent to 78.5c and Panoramic Resources adding 13.8 per cent to 16.5c.
In the energy sector, Woodside was up 2.3 per cent to a three-year high of $36.81 and Santos climbed 2.0 per cent to $7.85.
The big banks were higher, with ANZ climbing 1.6 per cent to $25.96, CBA up 1.3 per cent to $106.05 and NAB and Westpac both advancing 0.9 per cent to $32.70 and $24.32, respectively.
Insurance companies had a solid day. QBE rose 2.3 per cent, Suncorp added 2.1 per cent and IAG climbed 1.6 per cent to close at a one-year high of $4.98.
GrainCorp gained another 6.1 per cent to a three-month high of $8.88 as grain prices continued to surge following Russia's withdrawal from a deal that let Ukraine export grain via the Black Sea.
In tech, ReadyTech Holdings soared 28.1 per cent to a nearly one-year high of $4.15 after the education and workforce software company said it had received a tentative takeover offer of $4.50 per share from Australian private equity firm Pacific Equity Partners.
ReadyTech was considering the non-binding proposal.
Back in the mining sector, WA1 Resources soared another 60.5 per cent following the junior explorer's announcement last week it had discovered the valuable metal niobium at its drilling project in WA.
In less than a fortnight the discovery has sent WA1's shares surging by nearly 1500 per cent as they rocketed from 13.5c to $1.99.
The Australian dollar was buying 64.20 US cents, from 64.19 US cents at Monday's close.
ON THE ASX:
* The benchmark S&P/ASX200 index on Tuesday gained 113.4 points to 6976.9, a 1.65 per cent rise.
* The broader All Ordinaries climbed 114.8 points, or 1.63 per cent, to 7169.6.
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 64.18 US cents, from 64.18 US cents at Monday's close
* 95.14 Japanese yen, from 94.88 yen
* 64.84 Euro cents, from 64.54 Euro cents
* 55.81 British pence, from 55.35 pence
* 109.65 NZ cents, from 110.21 NZ cents.
