The former senator and secretary of state, who held the climate role for three years, will reportedly be involved in promoting Mr Biden's work on combatting global warming.
The 80-year-old informed his staff of the move on Saturday.
Americans will head to the polls in November to elect their next president.
Mr Kerry's departure follows the COP28 climate summit in Dubai, where he helped negotiate an agreement for countries to move away from using fossil fuels.
During his tenure, he also worked effectively with China despite strained diplomatic ties.
Alongside Beijing's top climate official Xie Zhenhua, he pushed for their two countries - the largest emitters of greenhouse gases - to work towards tripling renewable energy globally by 2030.
"The climate crisis is a universal threat to humankind and we all have a responsibility to deal with it as rapidly as we can," he said during a trip to the Chinese capital last year.
As secretary of state under President Barack Obama, Mr Kerry was key to brokering the crucial 2015 Paris climate agreement.
That deal saw nearly the whole world for the first time support a common strategy to cut the greenhouse gas emissions which cause global warming.
Mr Biden has pledged to cut US emissions in half by 2030, compared to 2005 levels. Two years ago, he passed $369bn (£290bn; €337bn) worth of green subsidies through Congress in a landmark bill.
While carbon pollution from greenhouse gases in the US went down by almost 2% last year - this was not fast enough to meet the 2030 target, according to an independent research firm.
Mr Kerry is still expected to attend the Munich Security Conference next month and attend the World Economic Forum in Davos next week.
By Ruth Comerford