Advocaat, who will become the Rangers' first foreign coach, forced the issue by signalling his intention to announce his future plans after guiding his present club, PSV Eindhoven, through a league game with Ajax on Sunday.
In a short statement, Murray confirmed that the 50-year-old Dutchman was always his first choice to succeed Smith, who is stepping down after leading Rangers to six of their nine successive Scottish titles.
"I am delighted that Dick Advocaat, one of the game's most respected coaches, has accepted the position of manager of Rangers," Murray said. "Over the past few weeks we interviewed a number of possible candidates for this position and from this it became quite clear that Dick was our first choice.
"As already stated, Walter Smith will continue to manage the club until the arrival of Dick from PSV on 1 July."
Murray, who was not prepared to reveal details of the length or value of the contract, said he felt obliged to make a statement to end speculation.
"I felt some pressure to make the announcement as I said I would reveal our choice near the start of the year and I feel this is the right time," he said.
Advocaat, who led the Dutch to the quarter-finals of the World Cup in 1994, has since won the Dutch championship and cup with PSV, but was faced with the prospect of several key players leaving the club at the end of the season.
Although his deal in Eindhoven ran until the middle of 1999, Advocaat exercised a clause in his contract that allowed him to annul the agreement should he receive a better offer elsewhere.
He said: "I have a very clear vision of the direction I wish to take the club and I look forward to working with everyone at Rangers to ensure that direction brings even more success to this great club."
Advocaat's arrival at Ibrox means Dutchmen will be guiding the attempts of both the main Glasgow clubs in their search for continental success. Advocaat's friend and former colleague, Wim Jansen, is head coach at Celtic.
While Rangers are chasing a record 10th successive title, their performances in Europe - with a couple of notable exceptions - have been disappointing. Earlier this season they suffered the indignity of being knocked out of both the Champions' Cup and the Uefa Cup early on, and the vice-chairman, Donald Findlay, was quick to point out this was another factor in the choice of Advocaat.
"He is a man with enormous experience in Europe and I think the Rangers supporters should be very excited about him bringing that experience to bear on our game from a European standpoint," Findlay said.
"He regards Rangers as a great club and a great challenge, and I think he appreciates that for a club of our size, our success rate in Europe in recent years has not been acceptable. He is looking forward to trying to improve that as well as maintaining domestic success."Reuse content