Dr Lowe will be replaced by Michele Bullock, the current deputy governor of the central bank, when he finishes on September 18.
Ms Bullock has served as deputy governor since April last year after a near four-decade RBA career, which has included several senior positions.
Prime Minister Anthony Albanese said Ms Bullock was "eminently qualified" to lead the national institution.
"Michele will be in an important job at an important time with the challenges we face globally," he said on Friday.
Ms Bullock said she was deeply honoured to be appointed.
"It is a challenging time to be coming into this role but I will be supported by a strong executive team and boards," she said in a statement.
The prime minister thanked Dr Lowe for his seven years of service, particularly for his efforts to support the economy during the COVID-19 pandemic.
The government considered a shortlist of candidates that included Ms Bullock, Treasury secretary Steven Kennedy and Finance secretary Jenny Wilkinson.
Treasurer Jim Chalmers said Ms Bullock represented the best combination of experience and expertise along with a fresh leadership perspective.
"This is the right call but it's not an easy call," he said.
Dr Lowe was at the helm of the bank throughout the turbulent pandemic period but it was during the recovery phase that his leadership landed him in hot water.
His prediction interest rates would stay on hold at low levels until 2024 attracted criticism after the RBA lifted rates much earlier in response to fast-rising inflation.
The governor later apologised for not adequately communicating the caveats attached to his guidance.
Dr Lowe has also been in the top job throughout an independent review and confirmed the bank would act on most of the recommendations in a speech earlier in the week.
Dr Chalmers said Dr Lowe had handled the pandemic period in an "impeccable" way, noting that lengthening an RBA governor's tenure was an "exception rather than a rule".
Ms Bullock will have the challenging job of steering the central bank through a major reform era as well as the unfinished task of returning inflation to target.
Inflation has passed its peak but was still growing at 5.6 per cent annually in May, well above the two-three per cent target range.
Former treasury official and economist Steven Hamilton said Ms Bullock was the best option but there was a valid argument to bring in an outsider to "shake things up" in light of the review findings.
He told ABC TV the decision to go with an insider, who was still able to implement change but unlikely to "scare the horses", was the right one given the uncertain economic environment.
But Mr Hamilton said Dr Lowe should not be criticised for lifting interest rates to tackle high inflation as the RBA has been doing since May last year.
Grattan Institute chief executive officer Danielle Wood was not surprised Dr Lowe's term ended in light of the review findings.
"It would be very unfortunate, though, if it was in any way a reflection of very difficult decisions the bank has had to make over the past year," she said.
Opposition Leader Peter Dutton said he did not want a senior public servant appointed to the role, arguing that the relationships between senior ministers and top bureaucrats was too cosy.
But the treasurer said the opposition leader was "relentlessly negative" and now "bagging things that aren't even happening".
Dr Chalmers and Dr Lowe are still expected to travel to India on Monday for a meeting of the G20 finance ministers and central banks.
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