The 83-year-old emperor said last year that his age and health were making it hard for him to fulfil his official duties.
But there is no provision under existing law for him to abdicate and be succeeded by Crown Prince Naruhito.
The bill will now pass to the parliament, where it is widely expected to be passed.
It would be the first time a Japanese emperor has stepped down since Emperor Kokaku in 1817.
Chief Cabinet Secretary Yoshihide Suga told reporters on Friday that the government "hopes for the smooth passage of the legislation"
Akihito, who has had heart surgery and was treated for prostate cancer, has been on the throne since the death of his father, Hirohito, in 1989 and is loved and revered by many Japanese.
In a rare address to the nation in August, he said he was beginning to feel "various constraints such as in my physical fitness" which caused him to "contemplate on my role and my duties as the emperor in the days to come".
The emperor is constitutionally barred from making any comments on politics, so he could not say explicitly that he wanted to stand down.
The bill approved by the cabinet on Friday mentions the widespread public support for the emperor's wishes, Japanese media reported.
It says that on abdication, Crown Prince Naruhito would immediately take the Chrysanthemum Throne, but that neither he nor his successors would be allowed to abdicate under the same law.
The government will set the date for the abdication, which is expected to be in December 2018.