Conway made his T20I debut against West Indies in November last year. He recently hammered 99 not out against Australia in the five-match T20I series at home. He averages over 52 after 11 T20I matches.
Young, meanwhile, hit two one-day hundreds for New Zealand XI against Australia XI in 2019 before a shoulder surgery cut short his year.
While veteran opener Martin Guptill has been declared fit, Lockie Ferguson and Colin de Grandhomme were not considered for selection due to back and ankle injuries, respectively.
The three-match ODI series between New Zealand and Bangladesh will begin on March 20 and will be followed by an equal number of T20Is.
Reflecting on the team selections, New Zealand selector Gavin Larsen said:
"Devon, Will and Daryl are quality players and have enjoyed impressive seasons so far, and we're looking forward to giving them further opportunities to develop their game at this level. Whilst it's disappointing to lose a player of Kane's class, Tom has proven experience in taking the reins, and I know he's excited to lead the side.”
Incidentally, the first ODI in Dunedin will be Latham's 100th in the 50-over format for New Zealand.
New Zealand to start building towards 2023 World Cup: Gavin Larsen
Larsen added that the series would begin New Zealand's preparations in right earnest towards the 2023 World Cup to be held in India. He said in this regard:
"It's certainly been a while since we've played ODI cricket, with just four games since the 2019 Cricket World Cup campaign. We're now in a new World Cup cycle, and our attention has turned to building towards the 2023 tournament in India. This series is a great opportunity to begin laying those foundations and formulating the type of team and game-plan we think can continue our impressive run in this format."
While there have been some changes in the batting department, New Zealand's bowling retains a largely settled look with Trent Boult, Matt Henry, Tim Southee and Kyle Jamieson. Larsen said:
"The bowling group is a strong and experienced one and will be well complemented by the two seam-bowling all-rounders in Jimmy and Daryl. We've also taken the decision to carry just the one spinner in the squad, which is a reflection of the venues for this series and expected pitch conditions. It's great to have Bangladesh on our shores, and we know they'll bring a lot to the series.”
New Zealand ODI squad: Trent Boult, Devon Conway, Martin Guptill, Matt Henry, Kyle Jamieson, Tom Latham (c) (wk), Daryl Mitchell, Jimmy Neesham, Henry Nicholls, Mitchell Santner, Tim Southee, Ross Taylor, Will Young.