A poll by West Yorkshire Police Federation found 90% of officers in the force wanted the equipment rolled out to all frontline colleagues, while a separate survey found 86% of members of the public agreed.
It shows a marked rise since a similar survey was carried out by the Metropolitan Police Federation earlier this year, which found 75% wanted to see all officers issued with the stun guns.
Nick Smart, chairman of West Yorkshire Police Federation, said the poll was the first to be carried out since the three deadly terrorist attacks in the UK this year.
"Given the recent terrorist attacks in London and Manchester and the changing nature of threats faced by police officers nationally this was an important survey and has provided some clear results," he said.
"It is apparent that an overwhelming majority of police officers and the public we serve believe police officers should be routinely carrying a Taser when on patrol.
When asked about carrying guns, two out of three West Yorkshire police officers (65%) wanted to remain unarmed but said they would like to see a significant increase in the number of fully trained firearms officers.
The survey found 86% of officers felt that frontline officers carrying Taser routinely would keep the public safer while 56% of police officers said they would feel safer carrying a firearm.
West Yorkshire Police is the fourth largest force in the country, with around a third of officers taking part in the survey, amounting to more than 1,500.
Mr Smart said the results would help shape the future discussions with the force's senior management team over using Tasers, firearms and both police officer and public safety.
"West Yorkshire Police officers must have the appropriate equipment to keep themselves, their colleagues and the public safe.
"And it is also vital that we have the right number of officers with that equipment available when they are required."
'We're still reeling from our loss' - Dalian Atkinson's family speak of agony one year on from Taser death
The 48-year-old was fatally died aged 48 after being shot by a police Taser outside his father's house in Meadow Close, Trench, Telford, on August 15 last year.
Mr Atkinson's family said: "A year has gone by and we're still reeling from our loss. Dalian was our baby brother.
"Our determination to get to the facts and to see that appropriate action is taken will not be weakened by the passing of time. We're buckled in for the long haul."
The Independent Police Complaints Commission (IPCC) earlier revealed that three West Mercia Police officers have been interviewed under criminal caution and served with gross misconduct notices relating to his death.
But the IPCC says the investigation does not necessarily mean criminal charges will follow.
The watchdog said it has has been looking into the level and type of force used during the incident, and considering evidence from 15 other police officers and more than 15 members of the public.
Investigators have transcribed relevant police radio transmissions and examined police policies on the use of force.
Analysis of the Taser which was deployed on Mr Atkinson has been carried out.
While all investigative actions have been completed, the IPCC investigation report cannot be finalised until the full pathology and toxicology reports are provided.
Paramedics and doctors were unable to revive Atkinson, despite administering CPR on him for more than an hour after he was taken to hospital.
Monday's statement, issued by the charity INQUEST, renews the family's previous demands for answers over the use of force during the former player's confrontation with police.
Deborah Coles, INQUEST director said: “As the Atkinson family mark the first anniversary of his tragic death INQUEST are deeply concerned about the disturbing number of recent deaths across the country following the use of force by police officers. There is a legitimate lack of trust and confidence in the systems for holding police to account for potential criminality and wrong doing.
"That some of the behaviours and responses to these recent deaths are so familiar to those seen in previous contentious deaths suggests a deeply concerning lack of learning, change and accountability."
Mr Atkinson’s funeral was held in November and was attended by former Villa players Ugo Ehiogu, Ian Taylor, Steve Staunton, Gary Charles and Tommy Johnson, as well as former manager Brian Little.