The 41-year-old, from Crawley, West Sussex, is believed to have bombed a jail in Aleppo on 6 February.
The footage shows Majid next to a large armoured truck bomb that was driven into the walls of the prison.
His family said they believed he was in Syria for humanitarian purposes.
Anti-terror police searched Majid's house in Langley Green on Wednesday.
Officials have not confirmed his identity citing a lack of DNA evidence, although community sources in Crawley have confirmed to Mr Gardner that Majid is the man in the video.
Mr Gardner said: "The 43-minute video clearly shows Mr Majid from Crawley in Sussex, dressed in white next to the large armoured truck bomb, which he is believed to have driven into the walls of Aleppo prison on 6 February."
Majid is believed to have been responsible for the prison attack that resulted in inmates escaping.
By Frank GardnerBBC security correspondent
This video provides the final chilling proof that a Sussex man, loved by his family and friends, chose to blow himself up in Syria in the cause of jihad.
Abdul Waheed Majid told them he was going for humanitarian reasons.
But the video, apparently filmed in a wood in northern Syria last week, clearly shows him surrounded by armed jihadist fighters and next to the armoured truck bomb later rammed into the walls of Aleppo prison and detonated.
The suicide bombing has alarmed counter terrorism officials here in Britain as they fear that other jihadists who go out to Syria may come into contact with hardcore al-Qaeda operatives who may urge them to turn their attentions away from the Syrian regime and instead attack targets in the West.
The bombing, in the north of Syria, is thought to have been the first carried out in the country by a Briton.
People living near Majid's home told the BBC he left some weeks ago for Syria.
An al-Qaeda-linked rebel group, the al-Nusra Front, had named Majid by an alias - Abu Suleiman al-Britani.
Counter-terrorism police raided a second house in Crawley on Thursday, which was believed to have been occupied by one of Majid's close friends.
That house is also the former home of schoolgirl Sarah Payne's killer Roy Whiting, according to neighbours.
The South East Counter Terrorism Unit said there had been no arrests following the searches in Crawley.
The Manchester home of student Abu Layth has also been searched by police. He is believed to have been killed while fighting in Syria.
Inquiries are continuing into how Layth, whose family name is Khalid Raoufi, died. Greater Manchester Police have confirmed his family is not under investigation.

Having taken part in the show's 2015 Christmas special alongside Peter Capaldi and Alex Kingston, Lucas will reprise the role of River Song's former assistant Nardole.
"I'm chuffed to bits that Nardole is returning to the Tardis for some more adventures," Lucas said.
The star will appear in the opening episode of series 10, which begins filming in Cardiff on 20 June.
Steven Moffat, lead writer and executive producer, added he was "delighted and slightly amazed to be welcoming Matt Lucas back on to the Tardis - and this time it's not just for Christmas, he's sticking around".
"One of the greatest comedy talents on planet Earth is being unleashed on all of time and space."
Capaldi will return as The Doctor while Pearl Mackie replaces Jenna Coleman as his new companion, Bill, in her first major television role.
Lucas said he was looking forward to reprising his role in the sci-fi drama because he "loved acting with Peter and I'm excited to work with Pearl".
Also announced to be joining the series this year is Jekyll & Hyde and Sherlock star Stephanie Hyam.
Doctor Who will return to BBC One with a December Christmas special followed by a new series in 2017.
A video has been posted online showing British man Abdul Waheed Majid, who is thought to have carried out a suicide bombing in Syria, the BBC's security correspondent Frank Gardner has said.
[NEXT_CONCEPT]
Matt Lucas is set to return to Doctor Who for its 10th series.