Media reports said that Wahab, who was born in Iraq but became a Swedish citizen in 1992, staged the attack on the eve of his 29th birthday.
He had lived in Britain for a number of years, prosecutor Tomas Lindstrand said, adding that his wife and three children still lived there.
Reports in Britain said his wife Mona, known as Umm Amira, runs a company called Amira Makeup and Hair which offers services including bridal make-up and hair styling.
When he was about 10, Abdelwahab and his family reportedly fled war-torn Iraq to settle in Tranaas, population 18,000, some 200 kilometres (125 miles) south of Stockholm.
"From Tranaas to Jihad," said Monday's Expressen tabloid, which published a full-page photo of a young, smiling Wahab wearing a typical Swedish high school graduation hat.
It said Abdelwahab had grown up in "a light red house" in Tranaas with his mother, father and two sisters, adding that the family had no problems adjusting to life in Sweden.
"He was just like any other young man. He loved life, he had lots of friends and was out and partied just like anyone else," acquaintance and Tranaas resident Jean Jalabian told Expressen.
"He drank alcohol and had girlfriends. It's really strange that he would do something like that," Jalabian said.
Aftonbladet meanwhile described "The terrorist from Tranaas" as a family-oriented basketball player with a lot of friends, beneath a smiling school picture of him.
A former teacher told Aftonbladet the young man spoke excellent Swedish, and was "an honest, friendly person with many friends."
But Abdelwahab drastically changed when he left Sweden in 2001 to complete a bachelor's degree in sports physiotherapy at the University of Luton -- now the University of Bedfordshre -- from which he graduated in 2004.
He became interested in radical Islam in the town just north of London, where he met his wife, reportedly the same age as him and also with Swedish nationality.
"He got to know an Egyptian imam at the mosque in Luton," a friend of the family told Expressen, adding that during his time there "he became another person. It's hard to say how. He changed and became more restrictive."
When he returned to Sweden in 2005, he had a beard, cut contact with his old friends and led a withdrawn life. He never settled back into Swedish life and went back to Britain, only sporadically visiting his family in Tranaas.
The chairman of the Luton Islamic Centre told AFP Monday that he had met many times with Abdelwahab to confront his extreme views and that his behaviour had alarmed fellow worshippers.
Abdelwahab was "a bubbly character who was quite respected, but that was before I knew what he was up to," said Qadeer Baksh, adding his final confrontation with Wahab came in 2007.
Aftonbladet said he showed his new opinions online, posting radical religious views on the war on Iraq and calling for a boycott of Denmark on his Facebook page in Arabic.
His status updates were often prayers, and he had uploaded videos with Islamist messages to his page, the tabloid said.
He was also searching for a new wife "who accepts Allah's religion and who is not against me having another wife" on a Muslim contact website, Expressen wrote.
In November he bought the car which he blew up on Saturday, slightly injuring two people, investigators said, after returning to Sweden a few weeks before.
In a threat he sent Swedish news agency TT and intelligence agency Saepo, Abdelwahab asked his family for forgiveness for lying to them.
"I never went to the Middle East to work or make money," he said. "I went there for jihad."
"It wouldn't have been possible to tell you who I really was. It wasn't very easy to live the last four years with the secret of being ... as you call it, a terrorist," he said.