Care has made 187 appearances since joining Quins in 2006.
The 28-year-old is in England's World Cup warm-up squad, but has not started for his country since November 2014.
"In Danny we have a player who, to me, epitomises how we play and what we are known for as a team," said Quins director of rugby Conor O'Shea.
"In making him captain we are making a statement as to how we intend to play and challenge for the title again."
Prop Marler was only appointed Harlequins skipper last summer, taking over from England captain Chris Robshaw.
The south-west London side finished eighth in the Premiership table last season and went out in the group stages of the LV= Cup and the European Champions Cup.
Care, who has won 51 Test caps, said he was "incredibly proud and honoured" to be asked to lead the side.
"I want to do the captaincy role justice, like so many other great captains who have done the job before me," he said.
"It will be great to have the experience of other leaders like Chris Robshaw, Joe Marler, Nick Easter and Nick Evans as well as Mike Brown around me.
"I know they will make my job a lot easier and support me in the role both on and off the field."
Harlequins have appointed England scrum-half Danny Care as their new captain, replacing international team-mate Joe Marler.