The former MSP is to stand in the constituency currently held by Ian Murray.
He stood in the Edinburgh Southern seat in 2016 but was not elected losing to Labour.
Edinburgh South was the only seat in Scotland to stay Labour when the SNP won 56 out of Scotland’s 59 Westminster seats two years ago. Mr Murray has said he is confident he can win again.
During his time at Holyrood, Mr Eadie was parliamentary liaison officer for First Minister Nicola Sturgeon and also convener of the parliament’s infrastructure committee.