It said a detailed, time-bound plan for implementation should be outlined as the move could improve safety and efficiency.
A plan for the system has been in place since 2007 but prescribing is still paper-based in Welsh hospitals.
The scheme must be in place by 2023, but the WAO wants it brought in sooner.
WAO director David Thomas said a number of the NHS staff auditors spoken to cited "frustration" that it was taking so long to bring in an electronic prescribing system in Wales.
He said implementing one would result in a "much more effective and efficient system within hospitals".
The report also looked at other areas of prescribing and found there were some safety issues caused by incomplete medicine information on paper drug charts, including some which did not have information about patients' drug allergies.
There were also some instances where notes were unclear about whether patients had received the doses they were due.
The report also looked at how new medicines were chosen and although there is a national process for appraising new drugs, it found there were three instances where decisions had been taken outside that process.
The WAO would not provide details of the cases, but Mr Thomas said where new drugs are given there needed to be very clear reasons for doing so.
The report also found that while NHS Wales was taking steps to improve prescribing in the community, there was scope to further improve quality and costs.
It said health bodies were working together well to improve the way medicines are prescribed and managed, and in hospitals, pharmacy services were rated highly by staff.
However, auditors highlighted problems with medicine storage and gaps in information about drugs.
A Welsh Government spokesman said it was pleased the report recognised there were many good aspects of medicines management in Wales.
It added that since last year, it had made good progress on a number of earlier recommendations by the auditor general, and it would respond to the latest advisories shortly.
Responding to the report, Nick Ramsay, chairman of the assembly's public accounts committee, said it showed there was "still much to do to ensure the safe and cost effective use of medicines in Wales".

Gubbins (109) hit 15 boundaries as he enjoyed a 198-run partnership with opener Sam Robson (99).
Robson fell one run short of a fourth ton of the season, being bowled by Joe Leach (4-64) for 99 as the Somerset bowlers remained accurate.
Despite a middle-order wobble, Paul Stirling (85) played solidly as Middlesex reached 407-9 at stumps.
Resuming on 139-0, Robson and Gubbins continued their excellent opening partnership before Robson was dismissed.
Gubbins brought up his century from 208 balls before nicking Jim Allenby (3-51) to Marcus Trescothick at slip.
There was some hope for Somerset as Middlesex lost four wickets for 39 runs, but Stirling steadied the innings.
He fell to Leach five overs before stumps after pushing Middlesex into a lead, but a draw still looks the most likely result.

HM Revenue & Customs said the plant, on the outskirts of the city centre, could have cost taxpayers nearly Â£138m a year in lost duty and taxes.
Four lorry loads of tobacco, cigarettes and packing materials have been seized.
Ten men, aged between 26 and 40 from Brazil and Paraguay, were detained on suspicion of immigration offences.
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Customs officials said the building was kitted out with machinery able to produce and package cigarettes on an industrial scale.
The raid took place over several days last week but details have only just been released.
A number of men were detained by immigration enforcement officers.
A nearby residence was also searched.
Stuart Taylor, HMRC's Fraud Investigation Service assistant director, said: "Tobacco fraud costs the UK Â£2.4 billion a year in lost tax, money that should be funding vital public services in the UK."
Sajeela Naseer, Birmingham City Council's head of trading standards, said the investigation into the cigarettes recovered was continuing.
The NHS in Wales must speed up plans to introduce an electronic system for prescribing drugs, a Wales Audit Office report has said.
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Nick Gubbins scored his first Middlesex century as their batsmen closed down Somerset's commanding total at Lord's.
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A suspected illicit cigarette-processing factory in Birmingham, thought to be capable of producing 35 million a month, has been shut down.