They said it was “a big step forward” in their campaign for justice for the 24-year-old who died after being stabbed in Stourbridge in August 2017.
Following a meeting with senior force representatives, the relieved family say West Yorkshire Police will be carrying out the review of the initial inquiry.
Last year Lloyd House announced an independent review of its investigation into the case, which saw Kobe Murray acquitted despite admitting he had stabbed Mr Passey, from Quarry Bank.
West Midlands Police said: "Today we met with Ryan's family to update them on the independent review of our investigation into Ryan's tragic death.
"We were pleased to be able to tell them that West Yorkshire Police have agreed to carry out that review. We will continue to keep Ryan's family updated."
Following the meeting on Friday family friend and spokesman Jason Connon said: “We were told that West Yorkshire will now be the reviewing force. We were pleased with that.
“We had a frank and honest meeting about our concerns with West Midlands Police and the manner in which we were dealt with in the past.
“We came out of the meeting with more than we have had from them in the last four years of trying. We have also been given access to the full review document which we will be able to check and respond to in due course.”
“It was an open and transparent meeting. It shouldn’t have taken so long to come about. It was inhumane.
“This is another big step forward for justice and for Ryan Passey’s family.
“We have been told that the conversations have already started with the West Yorkshire force which will contact us over the matter.
“Ryan’s family are very relieved after a what has been a very long journey.
“The point which has made the difference is that we had a civil ruling which was a big step forward in the campaign. People finding themselves in similar positions need to be aware that there is another way to get justice for their loved ones.”
Accused man Kobe Murray was cleared of both murder and manslaughter at a trial the following year after claiming he had acted in self-defence. Mr Passey’s family has since won a civil case against Mr Murray – now 23 and known as Kareem Gayle - after a judge delivered a verdict of unlawful killing.