The seat is currently held by Christine Grahame for the SNP. At the last election in 2016 she had a majority of 5,868 over the Tories, with Labour in third and the Lib Dems fourth place.
Mr May, originally from Inverclyde, has lived in the Lothians for the past 25 years.
He said: "Prior to the boundary changes, the Scottish Liberal Democrats had a long record of success here.
"Our high streets and town centres - the beating heart of our communities - need urgent help. This was apparent before the pandemic, but even more so now. Online commerce can bring tremendous benefits, and is here to stay. We need to focus on how growing online spend can coexist with a vibrant local economy, and work to restore community feeling.
"Issues like these, which affect us in our daily lives, are being pushed down the priority list. We're subjected to a confrontational power struggle being played out between Holyrood and Westminster, while the rest of us would prefer to focus on better public services and raising standards in our schools and hospitals.
"I'm looking forward to getting stuck into the campaign. By their own admission, a divided Tory party has mishandled Brexit, driving Scottish voters in desperation towards nationalism, while the opportunist and populist SNP seeks to compound the disaster of Brexit by withdrawing from the UK completely.”