Murphy has been handed QPR's number 26 shirt and manager Neil Warnock believes the Waterford-born goalkeeper is an important addition to the squad.
"I am delighted," Warnock told the club's official website.
"You need three senior keepers for the Premier League and we've got that now.
"Brian has had a super couple of weeks with us and was instrumental in us winning the Cup [Trofeo Bortolotti pre-season tournament] in Italy.
"He is a very capable understudy to Paddy, so him and Radek will offer great competition for the coming season.
"It was great to be able to have a good look at him before he signed.
"He fitted in so well with the rest of the squad during pre-season, and I could tell within two days that he was the one for us.
"His attitude is first class and he's got great mobility. He's got everything that we need."