The Scottish National Party's Alex Neill has suggested that the lord advocate's handling of the Shirley McKie fingerprint case has forced the move.
The case of Ms McKie is still being examined by Holyrood's justice 1 committee.
The former detective, from Troon, Ayrshire, was awarded Â£750,000 in compensation earlier this year.
It following a campaign after she was cleared of perjury when a print found at a murder scene in 1997 was wrongly identified as hers.
Ms McKie's father Iain also said his daughter's case and the possibility of a retrial in the Lockerbie case could be behind the lord advocate's departure.
But Lord Boyd, who has been the longest serving lord advocate for more than a century, insisted it was just time to move on.
Elish Angiolini has been tipped to take up the post
Ms Angiolini, 45, was born in Govan, Glasgow, and served as a deputy procurator fiscal in Airdrie for eight years before being seconded to the Crown Office in Edinburgh.
Her career then saw her working as a senior depute fiscal in Glasgow, before returning to the Crown Office as head of policy at a time when the department was preparing for devolution and the introduction of the European convention on human rights.
She then became the first woman, the first non-advocate, and the first procurator fiscal to hold the post of Solicitor General for Scotland when she was appointed in 2001.
Nationalists have called for the next lord advocate to be independent of the Scottish government.
Currently the lord advocate is both the head of Scotland's prosecution service and the chief legal adviser to ministers.
SNP justice spokesman Kenny MacAskill said: "Scotland's justice system needs an independent, professional law officer, not another hired politician."
And Liberal Democrat justice spokesman Jeremy Purvis argued that the resignation provided an opportunity to review the constitutional role of the position, describing the current situation as a "clear constitutional anomaly".