Hull boss Steve Bruce has made Austin one of his top transfer targets this summer and has been chasing him for several weeks.
Talks have been ongoing between both clubs as they haggled over Austin's price-tag, but now a fee has been agreed and Austin has been given permission to hold talks and undergo a medical with Premier League new boys Hull.
Austin has just 12 months remaining on his current deal and with no indication that he will sign a new deal Burnley have been forced to cash in on him.
The 24-year-old has established himself as one of the best strikers in the country since being plucked from non-league football by Swindon four years, netting 82 goals in 155 games for Swindon and Burnley.
Bruce is now hoping to tie up a deal for Austin as he continues his plans for the new season in the Premier League.