Dawson will lead the Crows in just his second season with the South Australian club after Sloane relinquished the role after four years at the helm.
Sloane, who turns 33 next month, is on the comeback trail after having a knee reconstruction last April.
"The time is right," Sloane said in a statement on Saturday.
"We have been talking about this for five to six months and I could 100 per cent keep going as captain but there is someone else who is ready to take the club forward."
Dawson joined the Crows last season after being selected by Sydney in the 2015 draft and playing 64 games for the Swans.
The SA-born 25-year-old was summoned into Adelaide's leadership group midway through last season and was runner-up in the club champion award.
"I could not be more excited to captain the club I barracked for growing up as a kid," Dawson said.
"It was surreal to pull on the guernsey last year and now this is a huge honour.
"Everyone at this club wants to win and have success and do it as quickly as we can, so I'm honoured to have the responsibility of driving that."
The Crows have missed the finals since being losing grand finalists in 2017 but coach Matthew Nicks praised the leadership of Sloane, who was appointed co-captain with Taylor Walker in 2019 and assumed the role by himself the following year.
"Rory has been a 'follow me' captain who puts his head in the hole on game day and has never asked anyone to do anything he wouldn't do himself," Nicks said.
"He has led our club brilliantly through some very challenging times and never let us down.
"But now is the right time to pass the baton to our next captain ... Jordan is ready because in key moments he steps up and delivers, particularly on-field.
"We identified him as having leadership qualities when we recruited him from Sydney and they have shone through in the past 18 months with us."
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