Last month, Lloyds Banking Group announced it would be launching the review, following a fraudulent scam perpetrated by former HBoS employees.
Griggs will examine whether any small businesses should receive payouts in the wake of the scheme, which drove some firms into the ground and eventually saw HBoS incur losses in the region of £250m.
Lloyds said Griggs' role "will be to agree the scope, methodology and individual case outcomes of the review in order to ensure fair outcomes and that the review is undertaken effectively".
Griggs is currently a board member and chair of the audit committee of Lenlyn Group, as well as board member of Audit Scotland, and member of the audit board to the auditor general for the States of Jersey.
Previously, he was chair of the CBI’s UK SME Council, a non-executive director of the Scottish government and chair of the Scottish government’s independent Regulatory Review Group.
Griggs, who has been awarded the Order of the British Empire for services to Scottish industry twice, has also participated in several reviews. He reviewed the SME appeals process for businesses appealing against credit being declined, the Lending Code and the branch closure programme for the BBA.
In February, the two former HBoS bankers and four other individuals responsible for running the scam were jailed for almost 50 years.
Lynden Scourfield, David Mills, Michael Bancroft, Tony Cartwright, Mark Dobson and Mills’ wife Alison were all found guilty of corruption, fraudulent trading and money laundering at Southwark Crown Court this year, following a five month trial.
Lloyds, which rescued HBoS in 2008, has apologised for the “distress” caused by the scandal.