They join South Australian captain Travis Head but leg-spinner Adam Zampa and Chadd Sayers – who made his Test debut earlier this month – were overlooked.
Carey made his debut for Australia as wicket-keeper in a one-day international against England in January and then played five T20 internationals after a successful BBL season with the Adelaide Strikers.
Richardson finished the international season strongly in T20 games against England and New Zealand. He played the last of his 15 one-day internationals against India in September last year.
Head, 24, is yet to make his Test debut but has now played 34 ODIs and 10 T20I and captained the Adelaide Strikers to the BBL title last season.
National Selector Trevor Hohns said he believed the squad is a “well-balanced list to represent Australia across all three formats”.
“This period is set to include a significant amount of limited-overs cricket, including the ICC Cricket World Cup 2019 in England and Wales," he said.
“For that reason, there has been a bit of a focus in this contracting period on white-ball cricket, as we look ahead to trying to win back-to-back World Cups.”
Players not awarded contracts as part of the initial squad of 20 can earn upgrades throughout the year by accruing 12 upgrade points. Players receive five points for a Test, two for an ODI and one for a T20I.
2018-19 CA men's contracts: Ashton Agar, Alex Carey, Pat Cummins, Aaron Finch, Peter Handscomb, Josh Hazlewood, Travis Head, Usman Khawaja, Nathan Lyon, Glenn Maxwell, Shaun Marsh, Mitchell Marsh, Tim Paine, Matthew Renshaw, Jhye Richardson, Kane Richardson, Billy Stanlake, Mitchell Starc, Marcus Stoinis, Andrew Tye.
OUT: Jackson Bird, Hilton Cartwright, James Pattinson, Steve Smith, Matthew Wade, David Warner, Adam Zampa
IN: Alex Carey, Shaun Marsh, Tim Paine, Jhye Richardson, Kane Richardson, Marcus Stoinis, Andrew Tye