The force's current Chief Constable John Robins QPM issued a statement on Friday following news of Sutcliffe's death.
The police chief said the effect of "language and terminology" used over the murder of sex workers in West Yorkshire was still felt by relatives of those women still alive today.
Attitudes described by many as "victim-blaming" were, Mr Robins said, "consigned to history" when it came to the force's approach to victim-based crime today.
It followed a plea by Richard McCann - son of Sutcliffe's first victim Wilma McCann - last month, calling for an apology.
Ms McCann was killed on playing field in Chapeltown, Leeds, in October 1975, before Sutcliffe went on to kill Emily Jackson, Irene Richardson and Patricia Atkinson, who had been working as sex workers at the time.
The murder of 16-year-old shop assistant Jayne MacDonald in 1977 prompted West Yorkshire Police to release a statement in which the force said "innocent women" were now also being killed.
A statement issued by Mr Robins on Friday afternoon said: “On behalf of West Yorkshire Police, I apologise for the additional distress and anxiety caused to all relatives by the language, tone and terminology used by senior officers at the time in relation to Peter Sutcliffe’s victims.
“Such language and attitudes may have reflected wider societal attitudes of the day, but it was as wrong then as it is now.
“A huge number of officers worked to identify and bring Peter Sutcliffe to justice and it is a shame that their hard work was overshadowed by the language of senior officers used at the time, the effect of which is still felt today by surviving relatives.
“Thankfully those attitudes are consigned to history and our approach today is wholly victim focused, putting them at the centre of everything we do.
“The well-documented Byford and Sampson reviews fully explored many issues. However, the reports did not fully address the issue of how victims were portrayed and described, which impacted on families, friends and wider public perception.
“I offer this heartfelt apology today as the Chief Constable of West Yorkshire Police.”
The investigation into the murders was the biggest and most exhaustive ever conducted by the force, who at the time were still using a paper filing system.
Detectives were thrown off course when a hoax tape was posted to them purporting to be from the murderer, who called himself 'Jack' and had a noticeable Wearside accent. John Humble was convicted in 2006 for perverting the course of justice after sending the tape. He died last year.
The 1981 report by Sir Lawrence Byford and a subsequent review conducted by former West Yorkshire Police Chief Constable Colin Sampson, identified failings made by the force at the time.
West Yorkshire Police Federation Chair, Brian Booth, meanwhile described Sutcliffe as a "monster" who should "rot in hell".
Mr Booth said: “As a child in West Yorkshire, when he was on his reign of terror, I can say his activities caused fear throughout the region.
“My heart goes out to all the families affected through the loss of their loved ones, but I personally will not be mourning the death of this monster.”
In a general statement in response to Sutcliffe's death, Mr Robins said: “I am sure the news of his death will bring back a range of mixed emotions and trauma for surviving victims and relatives of those whose lives he cruelly took away.
“Those who died and were assaulted, as well as those relatives who are still suffering today, are at the forefront of our thoughts and our condolences."
He added: "We can say without doubt that the lessons learned from the Peter Sutcliffe enquiry have proved formative in shaping the investigation of serious and complex crime within modern day policing.
“West Yorkshire Police is committed to ensuring that those harmed by crime are at the heart of what we do.”