Long-time team coach Wally Masur will fill in as Australia's interim captain, starting with the Cup tie against the Czech Republic in Ostrava in March, before handing the job to Hewitt at a later date.
Dual Grand Slam champion Hewitt, 33, who has won an Australian record number of Cup matches, said he will finish his career at his 20th consecutive Australian Open in 2016 before taking on the Davis Cup role.
"In December I started getting a lot more heavily involved with the new job and I just realised it's a really big job. I just can't do both roles," he said at the Australian Open.
"I'm officially stepping down from the Davis Cup captaincy. Wally Masur will take over as interim Davis Cup captain. Lleyton will then fill the spot when the time is right and ready."
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"I've thought long and hard. I plan to play the Aussie Open next year and most likely finish then," Hewitt said.
"Obviously for me the Davis Cup is something we've worked extremely hard to put ourselves in a position in the World Group where we have a genuine shot.
"I believe with the guys now we have a lot more options, a lot more depth. I feel like I can still put my hand up as a player and help the boys get over the line."