The SNP member for Edinburgh Eastern said he wanted to "pursue new challenges", but said he would remain committed to the independence campaign.
Mr MacAskill, 57, was justice secretary for seven-and-a-half years.
Opposition parties were critical of a number of his decisions during his time in office, including plans to abolish corroboration which were later dropped.
Mr MacAskill was succeeded by Michael Matheson in First Minister Nicola Sturgeon's new administration.
During his time in the role he also made the controversial decision to release Abdelbaset al-Megrahi, the only person convicted of the 1988 Lockerbie bombing, on compassionate grounds.
Mr MacAskill wrote to constituency members last night to tell them of his decision to step down in May 2016.
Speaking to the The National newspaper, the former solicitor said: "I'm proud of the commitment and efforts I made, but it will now be up to others to take things forward.
"I am not leaving parliament to retire, but am leaving to pursue what might be considered a third career.
"Independence for Scotland will remain dear to my heart and I will be committed to it."
Former justice secretary Kenny MacAskill is to stand down as an MSP at next year's Holyrood election.