There was an eight-fold increase in the time it took West Yorkshire Police to answer calls in 2015 compared to 2013, figures obtained by the BBC show.
In South Yorkshire the time tripled and more than doubled in North Yorkshire.
Police crime commissioner for West Yorkshire said extra staff had been recruited to bring response times down.
Figures, released under a Freedom of Information request, showed between April 2013 and April 2014 it took West Yorkshire Police on average 14 seconds to answer 101 calls.
That increased to one minute 46 seconds from April 2014 to April 2015, despite a drop in the number of people using the service.
Caller waiting times continued to increase in the eight months between April and November 2015.
Figures also showed the number of people hanging up before calls were answered had more than doubled from 5% in 2013 to 11% in 2015.
John Summerscale, a former special constable from Bradford, said he had experienced many delays.
"I was told by the police it should take four rings before someone answers but I've been waiting up to 20 minutes and still no answer."
Mark Burns Williamson, West Yorkshire police crime commissioner, blamed the delays on budget cuts but said extra staff had since been recruited to address the problem.
He said: "Such delays are unacceptable and I was being contacted by members of the public who weren't happy.
"We've got waiting times down now to between 18 and 60 seconds and there is a higher level of customer satisfaction with the service."
Elsewhere, it took South Yorkshire Police an average of 30 seconds to answer calls in 2013/14, rising to just under a minute and a half in 2014/2015.
In North Yorkshire, the length of time went up from 23 seconds in 2013/14 to just under a minute in 2014/2015.
Crime commissioners for both forces said improvements were being made including new technology and better online reporting of crimes.
Callers to the 101 non-emergency service at three Yorkshire police forces are having to wait longer to get through compared to two years ago.