The 22-year-old has joined on a one-year deal with the option of a second, and is Barrow's sixth summer signing.
He started his career at Fulham before moving to QPR where he failed to make a first-team appearance.
Fitzpatrick moved to Wimbledon in 2014 but only played 13 games, and had a loan spell in the National League with Torquay last term, scoring three goals.
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National League club Barrow have signed winger David Fitzpatrick following his release by AFC Wimbledon.