Cummins, who is also the Test captain, will now lead in two formats although it remains to be seen how frequently he takes charge of the one-day side in the lead-in to the 2023 World Cup given his workload.
"I have thoroughly enjoyed playing under Finchy and have learnt an enormous amount from his leadership," Cummins said on Tuesday. "They are significant shoes to fill although we are extremely fortunate to have a one-day squad with a huge amount of experience."
Finch's retirement, and the current composition of both the ODI and T20I teams, meant CA was limited in the number of options who could captain in both white-ball formats. CA had a preference to have just two national captains rather than three. As a result the option of having Cummins captain both the Test and ODI side while Finch continues to lead the T20I side was viewed as the best option.
Cummins has regularly been rested from the ODI team in recent times including the last two series that Australia played against Zimbabwe and New Zealand in August and September.
Speaking a few days ago, Cummins said he believes having a job share arrangement for the ODI captaincy could be managed.
"Playing every single game isn't realistic," he said. "It would be really seamless if you had a committee. The style of just about everyone in the team is really similar. We've got some great leaders in the team, we all get along great."
Australia's next ODI cricket is in late November with a three-match series against England. If Australia reach the T20 World Cup final there will be just a three-day turnaround to the opening game in Adelaide and with the Test summer starting shortly after, which begins a run of up to 15 Tests in eight months, that is the type of series Cummins could yet sit out.
After the England matches Australia's next ODIs are not until late March with series against India and Afghanistan.
"We are very fortunate to have a number of high-quality leaders and senior players across all formats," Ben Oliver, the head of high performance and national teams, said. "The board and selectors agree Pat is the ideal choice to lead the ODI team through the next period including the 2023 World Cup."
Chair of selectors George Bailey said: "Pat has done an excellent job since taking on the captaincy of the Test side and we look forward to him leading the one-day team to the 2023 World Cup in India."
However, the most likely to be his understudy would be Carey who stepped in as ODI captain last year on the West Indies tour when Finch was injured.