The benchmark S&P/ASX200 index on Tuesday rose 77.8 points, or 1.01 per cent, to 7,778.1, while the broader All Ordinaries climbed 72.2 points, or 0.91 per cent, to 8,015.8.
The cash rate remains at 4.35 per cent, with the RBA leaving its language about the outlook for rate hikes unchanged, continuing the mantra that they're not "ruling anything in or out".
RBA Governor Michele Bullock said that a rate-hike was considered, though a cut was not on the table as uncertainty remained in the economy's outlook.
The process of returning inflation to target is unlikely to be smooth, the board said.
IG market analyst Hebe Chen said one of the things making it more difficult to predict inflation is that the RBA still only has the first-quarter inflation figures.
Inflation figures from second quarter, which she noted will be released before the board meets again in August, are more important than ever.
"The August meeting will be quite a crucial tipping point," Ms Chen told AAP.
"If the quarter two inflation continues to deliver another upside surprise, I think it will be the time that we will see another potential 25 basis point high-flow for the Australian interest rate."
Every sector in the ASX finished higher, with utilities the biggest gainer, rising 2.5 per cent.
NAB led the way for the four big banks, rising rose 2.1 per cent to $36, followed by CBA which climbed 2.0 per cent to $127.99. ANZ rose 1.5 per cent to $29.24 and Westpac gained 0.9 per cent to $27.22.
Toll operator Atlas Arteria jumped 5.1 per cent, with Transurban Group hopping up 1.6 per cent.
The miners were a mixed bag, with Fortescue dropping 5.2 per cent to $21.79, reportedly after a major institutional investor sold a $1.1 billion shareholding.
BHP rose 0.6 per cent to $42.80 and Rio Tinto climbed 0.9 per cent to $119.26
One Australian dollar was buying 66.13 US cents, up from 65.95 US cents at Monday's ASX close.
ON THE ASX:
* The benchmark S&P/ASX200 index on Tuesday gained 77.8 points, or 1.01 per cent, to 7,778.1.
* The broader All Ordinaries rose 72.2 points, or 0.91 per cent, to 8,015.8.
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 66.25 US cents, from 65.94 US cents at Monday's ASX close
* 104.73 Japanese yen, from 103.78 Japanese yen
* 61.73 euro cents, from 61.67 euro cents
* 52.20 British pence, from 52.06 pence
* 108.31 NZ cents, from 107.90 NZ cents
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