Figures show that the city suffers an average of two and a half such attacks a day, down from nearly six a day in the year before Sir Stephen House was appointed chief constable of Strathclyde Police in 2007.
Latest figures showed there were 903 knife assaults in the city in 2012-13. That has fallen 37% from a figure of 1439 a year before and 57% from 2138 in 2006-07.
Andy Bates, the police commander for the new Greater Glasgow division, said: "For many years, this city has had a reputation for a high number of knife crimes. But there has been a significant reduction."
He added: "There are still too far many people being stabbed or attacked."
Mr Bates linked the falling figures for knife assaults with the six-fold increase in stop and searches.
In November 2007, when Sir Stephen took over as Strathclyde Police Chief Constable, there were 4356 stop-searches carried out in Glasgow. In November 2012, there were 26,669.
Stop-search tactics have now been rolled out across Scotland.
Some human rights advocates have expressed concerns about the policy - which sees thousands of innocent people inconvenienced.
Mr Bates, however, is convinced stop-searches, along with saturation policing by yellow-jacketed officers in trouble spots, is driving down knife and other violent crime.