However, more needs to be done as thousands of migrants are still stranded on the Greek islands after their arrival, according to the report.
Many of those affected are unaccompanied minors, say the auditors, and more should be done to help them.
Speaking at a news conference in Brussels on Wednesday, where the report was unveiled, Hans Gustaf Wessberg said, "At the end of 2016, there was still a shortage of adequate facilities to accommodate and process unaccompanied minors in line with international standards, both in the hotspots and at the next level of reception."
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Wessberg, one of the two members of the European Court of Auditors responsible for the report, said, "This issue needs to be addressed as a matter of urgency."
Responsibility for border control and asylum processing lies primarily with the member states.
The European Commission introduced the hotspot approach to help Greece and Italy cope with the sudden dramatic increase in migration during 2015 and 2016.
It provides support aimed at ensuring irregular migrants are identified, registered and fingerprinted on arrival and then moved on to the relevant follow up procedures.
The auditors found that the approach had helped improve migration management in Italy and Greece under very challenging and constantly changing circumstances.
Although setting up the hotspots took longer than planned, they increased the two countries' capacity to receive migrants, improved registration procedures and strengthened coordination among the various agencies involved, said the report.
Nevertheless, despite considerable EU support, the auditors still found that reception facilities in both countries were not adequate to properly receive (Italy) or accommodate (Greece) the number of migrants arriving.
The hotspot approach, they said, further requires that migrants be channelled into appropriate follow-up procedures - a national asylum application, relocation to another member state or return to the country of origin.
But these follow-up procedures are often slow and subject to bottlenecks within the member states' responsibility, said the EU auditors.
In Greece, new arrivals have, since March 2016, no longer been allowed to leave for the mainland but instead must lodge their asylum application at the hotspots.
Also, relocation is no longer an option, and returns are slow. As a result, there are still more migrants arriving at the hotspots than leaving, and they are seriously overcrowded. In Italy, as migrants receive better information about relocation, more candidates have been identified, and the auditors warn that the main problem now is a shortage of pledges from member states.
By September 2016, only 3809 formal pledges had been provided by member states to Italy, against the overall commitment made to relocate 34,953 people.
The auditors add that another major concern for both countries is a shortage of adequate facilities to accommodate and process unaccompanied minors, of whom there were an estimated 2500 in Greece and more than 20,000 in Italy by the end of September 2016.
The auditors make a number of recommendations for the Commission to assist the member states in improving the hotspot approach as regards capacity, the deployment of experts and roles and responsibilities.
To improve the treatment of unaccompanied minors, they recommend that the Commission should request the appointment of a child protection officer for every site.