Calum Muir, 45, became involved with the No Knives, Better Lives (NKBL) project in West Lothian after losing 21-year-old Nattalie in December 2010.
The campaign warns young people about the dangers of carrying a blade and encourages them to get involved in sports and the arts.
A Scottish Government pledge of £550,000 will now see the initiative offered in every local authority.
Mr Muir, from Whitburn, has toured schools and filmed a hard-hitting DVD about his daughter's murder since local police asked him to get involved.
He said: "My first thought was no - it was too late for me. But my daughter had a wee girl of just two and she's going to be brought up on the same streets.
"With the way things were with the knife culture, I thought 'I think I will get involved and support this campaign'.
"It seems it has been a massive success in West Lothian. We've had children going to guidance teachers and handing in knives and a couple of girls said they wouldn't carry knives again.
"To hear of even one knife being surrendered makes it all worthwhile for me. I really do welcome a national roll-out of the campaign."
Three people were jailed for the attack on Nattalie Muir in Whitburn, which saw her left in the street to die.
Since it began, NKBL has recruited 130 "peer educators" who discuss the dangers of knife carrying with young people and identify positive alternatives to violence.
Councils, police and youth groups are also involved in delivering the message to schools and communities.
Justice Secretary Kenny MacAskill said: "Since No Knives, Better Lives started in 2009, it has aimed to challenge attitudes to carrying knives and to work with young people to find alternatives to violence and make good decisions about their lives.
"There is no doubt that Scotland is a safer place than it was even a few years ago, with recorded crimes of handling an offensive weapon at their lowest level in 27 years, falling by 60% since 2006/07, and violent crime at a 38-year low.
"Education and prevention is fundamental to tackling the root causes of violence and crime. That's why the Scottish Government has provided more than £2 million of funding to No Knives, Better Lives in the past five years, and why we are committed to rolling out the programme across Scotland."
NKBL has previously operated in Clackmannanshire, East Ayrshire, Edinburgh, Glasgow, Inverclyde, North Ayrshire, North Lanarkshire, Renfrewshire, South Lanarkshire, West Dunbartonshire and West Lothian.
YouthLink Scotland supports the NKBL campaign, providing administrative services through a national delivery team.
YouthLink Scotland chief executive Jim Sweeney said: "The success of No Knives, Better Lives is a powerful example of the positive impact that youth work can have in helping young people deal with difficult situations and make good decisions.
"We will continue supporting the campaign as it is rolled out across Scotland, working in partnership with the Scottish Government and local authorities."