Maidenhead United’s prolific striker became a Barnet player after a fee was agreed between the Mapgies and the Sky Bet League Two club.
Tarpey has always spoken of his ambition to play in the EFL and at 28 gets his opportunity.
The former Farnborough and Hampton and Richmond player told the Barnet official website that he was thrilled to get his professional chance.
Tarpey has scored seven times this season after 45 goals last term as his team stormed to the Vanarama National League South title.
"We left it a bit late but I’m delighted to be here!” the striker said. “I’ve come here to score goals. Hopefully I can bring the same strike record to Barnet and help them push up the league.”
Tarpey has been wished luck this morning by a number of his Maidenhead United team mates on twitter.