The latest deal, which takes the Glasgow business up to seven practices across the central belt, is being funded by a six-figure loan from Royal Bank of Scotland.
Vishal Marwaha and Geoff McCullough set up MM Eyecare in 2007 and have steadily expanded its footprint through acquisition.
The pair also run the home visit optician service, Vision Care at Home, which operates in Scotland and the north west of England.
McGraths, which is based on Queensferry Street in the Scottish capital and which can trace its roots back to the 1930s, specialises in upmarket frames including hand-made models by Danish brand Lindberg, as well as products from fashionable designer names such as Prada, Oakley, Paul Smith and Ray-Ban.
Mr Marwaha, a former Great Britain and Scotland international hockey player, said: "When we saw McGraths, we felt it was too good an opportunity to pass up - it's an incredibly well-run business that specialises in niche, high end products.
"The business is in a visible location right in the centre of Edinburgh."
MM Eyecare has banked with RBS since starting up and has previously used the lender to fund a number of its acquisitions.
It returned again to RBS to secure further backing for the McGraths deal with the loan supported through the bank's participation in the Funding for Lending scheme.
The most recent abbreviated accounts at Companies House for MM Eyecare show a retained profit of more than £27,000 for the 12 months to March 31, 2013.
The balance sheet in the financial document shows the business had total net assets worth in excess of £381,000.
The directors believe the acquisition of McGraths will increase group turnover at MM Eyecare substantially in the coming financial year. Kevin McCormack, RBS relationship manager, said: "It's clear that the addition of McGraths to the MM Eyecare Ltd portfolio will make a big difference to the business in the future." Mr Marwaha said: "Kevin has been our relationship manager for two years now and as a healthcare specialist, we feel he understands us and our business and can introduce us to influential people in the industry."
MM Eyecare has its other practices in Bishopbriggs, Portobello, Bo'ness, Linlithgow, Stirling and Summerston in Glasgow. Mr Marwaha and Mr McCullough said they are continuing to look for opportunities to expand Vision Care at Home further into England.