Mr Atkinson died early on Monday morning after officers responded to an alert "for the safety of an individual" at a home in Meadow Close around 1.30am.
The 48-year-old was given medical treatment but died about 90 minutes later, West Mercia Police said.
Ipswich Town paid tribute on its Twitter feed, saying: "Terribly sad news about our former striker. Our thoughts are with Dalian's family and friends at this tragic time."
Sheffield Wednesday said on the social media site: "The thoughts of everyone at Wednesday are with the friends and family of Dalian Atkinson this morning. RIP".
Former team-mate Tony Daley, who played for Aston Villa at the same time as Mr Atkinson, tweeted: "Devastating news...RIP Dalian" with an image of a broken heart.
Another former player, Ian Taylor, said: "Just heard news re my old team mate Dalian. Deepest condolences to his family. Only spoke to him last week as well. Sad sad news."
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Mr Atkinson's father, thought to be in his 80s, lives in Meadow Close and the footballer was believed to have been visiting him when police were called.
Neighbours said the retired star, who drives a Porsche, was well-known among people in the street, making frequent visits to the short cul-de-sac.
Local resident Paula Quinn said Mr Atkinson appeared to be "almost staggering" in the street before he was Tasered.
Miss Quinn, who lives in a first-floor flat above a barber's shop, claimed Mr Atkinson went down "like a lead balloon" after being hit by the Taser.
The witness added: "I heard shouting and something smashing, which is what alerted me to look out of the window.
"I am feeling a bit sick knowing that the poor lad has passed. I don't care what anybody has done. Nobody deserves to die as a result of something like that."
West Mercia Police said in a statement: "West Mercia Police can confirm that officers responded to a report for the concern for the safety of an individual at approximately 1.30am this morning at an address in Telford.
"Upon arrival Taser was deployed and a 48-year-old man, who subsequently received medical attention, was pronounced dead at approximately 3am.
"West Mercia Police are unable to comment any further as the incident has been referred to the Independent Police Complaints Commission (IPCC) as is normal procedure, and will assist the IPCC with their inquiries."
Former Aston Villa footballer Dalian Atkinson has died after being Tasered by police (Anton Want/Allsport/Getty)
Mr Atkinson was a top flight striker in the 1990s, with a goal for league runners-up Aston Villa against Wimbledon, which followed a mazy run from inside his own half, being voted 1992-1993 goal of the season.
He went on to score at Wembley in 1994 as Villa beat Manchester United to lift the League Cup.
Starting his career at Ipswich he played for Sheffield Wednesday and Spanish team Real Sociedad before moving to Villa.
He scored more than 20 Premier League goals for the Birmingham side between 1991 and 1995 before going on to play less successfully for teams including Turkish side Fenerbahce and Manchester City.
He ended his career playing in South Korea in 2001.
A West Midlands Ambulance Service spokesman said: "We were called by West Mercia Police to an address in Meadow Close in the Trench area of Telford at about 1.45am this morning.
"An ambulance was dispatched and upon arrival found a man who had been Tasered.
"As he was being conveyed to Princess Royal Hospital, his condition deteriorated and he went into cardiac arrest.
"Despite the efforts of the crew and hospital staff, it was not possible to save him and he was confirmed dead at hospital, shortly after arrival."
His death follows that of ex-soldier Spencer Beynon in June, after he was Tasered by police in Llanelli, South Wales, after stabbing a dog and then himself.
Friends said he had suffered mental health problems after leaving the military.
Last year, police use of Tasers, which are intended as a non-lethal weapon, went up slightly towards the end of 2015 with 10,329 uses by forces in England and Wales, a two per cent rise on the previous year.
However, of those, 19 per cent (1,921) were discharges; a decrease of three per cent from the previous year.
Between January 2014 and November 2015, police forces in England and Wales used Tasers on minors at least 407 times, including 57 times against children aged 14 or younger.
Additional reporting by PA
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