The experienced right-back, 34, will team up with his former Solihull Moors boss Tim Flowers at the Hive Stadium, with the Bees sitting second-bottom of non-league's top tier.
Vaughan, who last summer returned to the New Bucks Head for his second spell at Telford, becomes the second player to depart the Bucks since the National North season was curtailed, following James Hardy, who joined Altrincham.
The all-action full-back appeared 17 times in all competitions for Gavin Cowan's side in the 2020/21 season, including 15 outings in the league.
He made his 200th appearance for the club in December, joining a select band in doing so since the club's formation in 2004.
The former Kidderminster, Cheltenham and Tranmere defender will see out the remainder of the campaign with the north west London club, with whom he has penned a short-term deal.
Like almost all of his Bucks team-mates, Vaughan signed a one-year deal at the club last summer. Striker Jason Oswell is the only player whose terms run until the end of next season.
Boss Cowan said: "During these unprecedented times we are having to adjust accordingly and so are the players. It’s a great opportunity for Lee to continue playing and staying sharp. We wish him a prosperous few months at Barnet."
Telford were 14th in National North before a majority voted for the campaign to be null and void due to concerns regarding funding.