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.

Andrew George, who was re-elected Liberal Democrat MP for St Ives in May, is one of four MPs to have tabled an amendment to the finance bill.
It follows the government's budget announcement that from 4 January VAT will rise from 17.5% to 20%.
Mr George wants the government to assess the impact of such a rise on businesses, charities and households.
The other three Liberal Democrat MPs who have put their name to the amendment are Bob Russell who represents Colchester in Essex, Mark Williams who is MP for the Welsh region of Ceredigion and mid-Wales and MP Roger Williams, whose constituency is Brecon and Radnorshire.
Mr George said: "I am not trying to trigger nuclear war and break up the coalition, it's perfectly normal for two parties to have different approaches and values.
"I just want to express my unhappiness with the move and have an open debate."
Mr George also said he hoped a government minister would respond to the amendment on Monday and added he would continue to look for opportunities to press his case.
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.
[NEXT_CONCEPT]
An MP from Cornwall is calling for an investigation into the impact of increasing VAT to 20%.