The 25-year-old Baggies midfielder, who had a 3 month loan spell at Turf Moor earlier this season, has signed a 3 year deal with the Clarets for a fee that could reach £250,000.
Albion will receive an initil fee of £175,000 for O'Connor and a further £75,000 should the the Clarets win promotion to the Premiership.