The member for Edinburgh Eastern said he is leaving the Scottish Parliament to “pursue new challenges”, but said he would remain committed to the campaign for independence.
MacAskill, 57, was succeeded by Michael Matheson as Justice Secretary in Nicola Sturgeon’s new administration after seven and a half years in the role.
During that time he made the controversial decision to release Abdelbaset al-Megrahi, the only person convicted of the 1988 Lockerbie bombing, on compassionate grounds.
He wrote to constituency members last night to tell them of his decision to step down in May 2016, the National reported.
The former solicitor told the newspaper: “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.”
Mr MacAskill was elected a Lothians list MSP in 1999 and 2003, before winning Edinburgh East and Musselburgh seat from Labour at the 2007 election.
In 2011, he was elected MSP for the newly named constituency of Edinburgh Eastern.
Regarded as one of the SNP administration’s heavyweights, he served as justice secretary from 2007 to November last year.
Before Holyrood he worked as a senior partner in an Edinburgh law firm and has written several books on nationalism in Scotland.
An excerpt from his letter to constituents, published in the National, said: “It is with a heavy heart that I have decided that it is time both for someone new and something new.
“Come next May I will have represented the constituency for nine years, and the wider area for 16 years.
“As with stepping down from ministerial office in November after seven and a half years as the longest service justice secretary, there comes a time when it is appropriate for fresh blood and also for new challenges.”
Mr MacAskill said he had always planned to stand down in 2016, even if Scotland had returned a yes vote in September’s independence referendum.
Fellow SNP MSPs paid tribute to Mr MacAskill on social media.
Culture Secretary Fiona Hyslop said: “Wishing Kenny MacAskill well for his future pursuits - his contribution to the success of the party of Government the SNP has been immense.”
Former education secretary Michael Russell said: “Sorry to hear Kenny MacAskill is standing down. Great long term colleague, fine speaker, strong Cabinet secretary - he will be missed.”
Tommy Sheppard, the newly elected SNP MP for Edinburgh East, said: “Just heard that my mate Kenny MacAskill is to leave Scottish Parliament. He’s put in quite a shift. Hard act to follow. Thanks and good luck.”