Advocaat, 69, and Dutch legend Gullit have signed contracts until the end of the year, the football federation said on Tuesday, admitting it was "a short-term" rescue mission.
Disciplinarian Advocaat returns for a third stint in charge, taking over from Danny Blind, who was sacked in March after the Dutch were beaten 2-0 by Bulgaria.
The shock defeat left the once-proud Dutch clinging to only the slimmest of hopes of reaching the World Cup finals in Russia next year.
Hans van Breukelen, the Dutch federation's (KNVB) technical director, told reporters at an at-times heated press conference that the KNVB had wrestled with "two scenarios".
"Either we decided to go with a long-term solution or we did everything we could to qualify for the 2018 World Cup.
"We decided to go for the second option and therefore we needed an experienced trainer, someone with authority."
Advocaat and Gullit will get extended contracts if the Dutch pull off a miracle and qualify for the World Cup.
Advocaat, who has also coached the UAE, South Korea, Russia as well as briefly Serbia and Belgium, previously managed the Dutch national side from 1992 to 1994 and 2002 to 2004.
The Netherlands, three-time World Cup runners-up, have endured a tough time in recent years, failing to qualify for Euro 2016 in France and now facing the prospect of being a humiliating World Cup no-show.
The defeat in Sofia left them fourth in qualifying group A, trailing six points behind leaders France.
Their next qualifying match is on June 9 against Luxembourg. Before that they have friendlies against Morocco on May 31 and the Ivory Coast on June 4.
Heated words were exchanged at the press conference over why former Manchester United manager Louis Van Gaal or current UAE trainer Henk ten Cate were not chosen for the job.
Ten Cate told Dutch media last month he had been offered the post but refused it, hinting he felt he did not have the backing of the whole team.
"I never said he would become" the coach, said Van Breukelen, and "now I'm glad that we did not end up choosing him".
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