Archie was a member of the successful 2011/12 youth team that reached the semi-final of the FA, partnering Steven Hewitt in midfield.
He won his first professional contract at the end of that season but the 2012/13 season was problematic due to injuries.
Fit again, he's played regularly in the development squad this season and just this week he scored the winner in a friendly against Chester at the Deva Stadium.
The West Yorkshire club have this afternoon confirmed the loan but there is no indication as to how long he'll be with them.
They travel to face MK Franchise tomorrow in the FA Cup. He will be able to play in that game, provided Burnley have given permission, should his loan have been completed before noon today.
The rule for the competition states that he must have signed by noon on the Friday previous to the date fixed for playing the round.
It's his first loan from the club and will hopefully provide him with his first opportunity of first team football for a side who are currently in 12th place in the Conference after winning promotion last season.
Update: Archie has been given permission to play for FC Halifax Town in the FA Cup and the loan is a youth loan until the end of the season.