Ex-Mansfield and York man Meikle, 28, finished last term at National League North Alfreton and exercised his option to join a higher-league club.
He has signed a one-year deal with an option for a further 12 months based on appearances, as have Parry and Harvey.
Parry joined in February, while Harvey has been at Barrow since 2012.
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Forward Lindon Meikle has joined National League side Barrow, who have also given new contracts to midfielders Andy Parry and Alex-Ray Harvey.