Liverpool accepted the Clarets’ bid to sign the 23-year-old in July, with Flanagan taking time to consider whether to leave his boyhood club.
But the full-back has now decided to make the move to Turf Moor, and will undergo a medical this weekend.
Allan Rodrigues, Taiwo Awoniyi, Lloyd Jones and Cameron Brannagan are also set to leave before the end of the transfer window.
Flanagan recently recovered from a nightmare knee injury that kept him out of action for 619 days, but Jurgen Klopp has advised him to spend 2016/17 under Sean Dyche.
Klopp is believed to see Flanagan playing a big role in his long-term plans, but wants the defender to improve his fitness first.
It remains unclear whether Burnley have accepted the 75 percent playing clause the Reds have negotiated in other loan deals this summer.
This would mean Flanagan is required to play in three-quarters of the competitive fixtures he is available for during his time with the Clarets, providing valuable game time.