Griggs, who was appointed after consultation with the Financial Conduct Authority, will assess the cases of British companies that were affected by the Reading HBOS fraud.
The fraud involved two former bankers at HBOS who siphoned off money from struggling businesses, which were clients of the mortgage lender, to fund lavish holidays.
Six people were jailed earlier this year over the case, which is estimated to have cost victims £245mln.
Griggs has overseen previous reviews in the banking industry, including looking into ways to minimise the impact of branch closures and assessing the code for how banks pledge to lend to small businesses and consumers.
The protocol on branch closures for the British Bankers’ Association drew criticism over how quickly lenders were cutting back on branches and in areas where people may struggle to use online banking.
"Professor Griggs was selected for his experience in overseeing high profile reviews of a complex nature and for his clear understanding of SME businesses, as well as his track-record in ensuring the principles of fairness are followed in a number of joint Government, banking and industry initiatives," Lloyds said in a statement.
“The role of the independent reviewer 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.”
Lloyds, which rescued HBOS in a takeover during the 2008 financial crisis, said it has written to the majority of customers affected by the fraud since the announcement of its review last month.
The news follows the bank's statement last month that it has set aside a further £350mln to cover claims for mis-sold payment protection insurance (PPI) after the financial regulator moved its deadline for new complaints. The Financial Conduct Authority last week announced it was moving its cut-off date for new PPI complaints to August 2019 from a previous deadline of June 2019.
The further provision Lloyds has put aside to cover the extra two months will be included in the lender’s first quarter results.
Shares fell 0.45% to 69.03p in afternoon trading.