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I had a Blogger site that was recently migrated to the fabulous Jekyll (which this website is running on too!).
Jekyll provides migration tools for Blogger, Wordpress and others.
Export from Blogger to get all your posts in a XML file. eg. blog-05-12-2016.xml
Then run in your Jekyll folder:
ruby -rubygems -e 'require "jekyll-import";
JekyllImport::Importers::Blogger.run({ "source" => "./blog-05-12-2016.xml" })'
It will parse the XML and create the posts in your Jekyll folder.