The promising 23-year-old joins after the clubs agreed a fee believed to be in the region of £1.5million.
The full-back, son of former Birmingham City striker Paul Furlong, has signed a four-year deal at The Hawthorns.
He played 20 Championship games for QPR last season after previous loan spells with Northampton Town, Cambridge United and Swindon Town.
He is the latest recruit to join after the arrival of new head coach Sleven Bilic, following the arrivals of Filip Krovinovic, Kenneth Zohore and Semi Ajayi.
Furlong's arrival will allow unwanted full-back Allan Nyom to be sold to Spanish club Getafe, and help plug the gap on the right side of defence.
Mason Holgate played there during the second half of last season, and has returned to parent club Everton.
However, the Baggies are keen to bring Holgate back on loan next season and are waiting to see if the Merseyside club are willing to let him leave again.
Signing Furlong would not cool their interest in Holgate, who can play centre-back as well as right-back.
The Baggies are also interested in former Hawthorns academy player Romaine Sawyers, and had a £2.2million bid rejected by Brentford, who would want £3m for the 27-year-old, who restored his career at Walsall after leaving Albion, where he spent three years.
Sawyers then followed current Villa boss Dean Smith to Brentford, and has been at Griffin Park for three years.