The trio had missed out on selection for the team's last 50-overs assignment, against Sri Lanka in March, for failing to meet the team management's fitness standards.
Allrounder Chase and middle-order batter Hetmyer featured in the Test and T20I legs, respectively, of the just-concluded home series against South Africa, but Cottrell, the left-arm quick, has not played for West Indies since November 2020.
Batting allrounder Kyle Mayers, who made his ODI debut against Bangladesh earlier this year, and offspinner Kevin Sinclair, who is uncapped in ODIs, didn't find a place in the squad, but Anderson Phillip, the fast bowler who made his ODI debut against Sri Lanka in March, kept his place in the side.
"This squad is coming off a comprehensive series win against Sri Lanka which should boost their confidence going into what is expected to be a tougher contest against Australia, chief selector Roger Harper said. "The return of Shimron Hetmyer, Roston Chase and Sheldon Cottrell adds greater depth and experience to the squad.
"Playing in familiar home conditions, hopefully will bring out the best in each player thereby enabling the team to perform at a consistently high standard."
The ODIs will be played on July 20, 22 and 24, and will be part of the ODI Super League for automatic qualification for the 2023 World Cup in India.
Before the ODI series, West Indies will face Australia in five T20Is in St Lucia, from July 9 to 16. The same squad that featured in the T20Is against South Africa is set to play this series and the upcoming one against Pakistan as well.