The 21-year-old has signed a three-year deal at Underhill, just six months after joining Dartford following his release from Southend.
Director of football Paul Fairclough told Barnet's website: "Harry Crawford is a young player who I have monitored closely this season because he is a talented forward who already has experience in the Football League.
"It would have been irresponsible of Barnet Football Club to not take notice of a player who lives locally and has the goalscoring record in the Conference Premier that he has.
"A player of this quality in the Conference would command a lot of money but we have captured Harry for free.
"His potential is huge and under the guidance of Edgar Davids and his management team I believe they can make him a complete player during his time here.
"He has agreed a three-year contract with us and during that time we expect him to work extremely hard to make a name for himself at the club and in the Football League."