Born Gerald Harrison in York, Gee left school at 15 and studied at Art College. He took a job as an artist, working mainly with stained glass and for a while worked on the stained glass windows at York Minster. He played in a rock band in the evenings. The group were called 'Gerry B and the Hornets' before they altered the name to 'Gerry B and the Rockafellas'. When the group disbanded, Gee became a compere, then later a comedian.
In 1975, Gee met his future comedy partner, Les Dennis.
After 20 years in showbusiness, Gee got his television break on Who Do You Do?, an ITV showcase . The show gave the opportunity for up and coming entertainers and impressionists to impersonate a host of stars, including Robert Mitchum and Mick Jagger. Les Dennis also appeared on this show.
From April 1980 to July 1985, Gee was star guest on Russ Abbot's Madhouse. Les Dennis later became one of the cast in 1982 - it was during this year that Gee and Dennis formed a comedy double act. By this time, Gee was a huge cabaret star in the UK, selling out theatres and nightclubs by word of mouth alone. This was the show that included his most famous impression, as Coronation Street's Vera Duckworth in two-handers with Mavis Riley (played by Les Dennis).
In 1982, Gee appeared on ITV's talent show, Success, alongside a sixteen-year-old Lisa Stansfield, who was making her TV debut.
His take on John Cleese as eccentric hotel owner Basil Fawlty was acclaimed by Cleese himself as the "best he'd seen". Billy Connolly told his partner Les Dennis that he always wanted to meet Gee and regretted that he never did so.
When Gee perfected his imitation of Larry Grayson, Larry thought so highly of his impersonation that on many occasion, he praised Gee in public and on television for it. The pair became close friends and remained so until Gee's unexpected and untimely death.
On Saturday 7 April 1984, Gee and Dennis began their own TV comedy show, The Laughter Show (retitled, Les & Dustin's Laughter Show, for the third series). The first episode of a third and final series aired on Saturday 28 December 1985. The second episode had already been planned to be postponed for a fortnight, but it was during this time that Gee died. The series was resumed upon the request of Gee's family. In the summer of 1986, the third series of their Laughter Show was repeated uninterrupted as a tribute to Gee.
On Sunday 15 April 1984, when Tommy Cooper suffered a massive heart attack whilst appearing on ITV's Live From Her Majesty's, Gee and Dennis were the act that was billed to follow him. They performed onstage whilst attempts were being made, backstage, to revive Cooper.
In May 1985 Dustin fell ill whilst on stage at the opening night of a summer season at the North Pier in Blackpool. He carried on but after the show he was taken to hospital where a minor heart attack was diagnosed. Gee was also told that he had dilated cardiomyopathy and that he should take it easy. He didn't appear in the summer season for a month, but he returned on his birthday, to complete the run until the end of September, thus ignoring doctors who told him to take six months off. That autumn, Gee and Dennis recorded the third series of their Laughter Show - the first episode aired on Saturday 28 December 1985 but the rest of the series was postponed due to Gee's death.
From December 1985 to Wednesday 1 January 1986, Gee and Dennis appeared in pantomime at the Southport Theatre, Merseyside. On Wednesday 1 January 1986, Gee suffered a severe heart attack. They were playing the Ugly sisters in Cinderella, a role they had played two years before in Bradford, when they appeared with Russ Abbot. At the end of a scene, Gee suddenly clutched his left arm. When they reached their dressing room he said to Dennis "I think I am dying". He collapsed shortly after. Basil Soper, the show's company manager, revived him. Roger Edwards (his PA) accompanied him to Southport General Hospital.
On Thursday 2 January, Dennis and Edwards were by his bedside. Gee was unconscious but they both urged him to keep fighting and he raised a finger.
Gee woke up suddenly at 8am on Friday 3 January. He asked for a cup of tea and some ice cream. According to his family members who were with him, he was "quite chatty". He thanked them for coming and said that they must see him in pantomime when he recovered - he also asked where his watch was. He was sitting up for a while and it appeared as if he was going to survive and recover. However, later that morning he lost consciousness again and died at 12:45 p.m.
Russ Abbot said that he was devastated at the news, and called Gee a "Great trouper and entertainer."
Jim Bowen replaced Gee in the pantomime.
Dustin's funeral was held on 9 January at St Oswald's Church, at Fulford, York. Three hundred people attended. Famous names there were Elizabeth Dawn, Bill Tarmey, Thelma Barlow, Dana, John Hamp, The Krankies, John Birt and Les Dennis. Floral tributes and wreaths were sent by Danny La Rue, Jimmy Tarbuck, Sarah Greene, Mike Smith, Des O'Connor, Tom O'Connor, Jim Bowen, Les Dawson, Bill Cotton, Larry Grayson, Ernie Wise, Lord Delfont, Russ Abbot and Jeffrey Holland. He was later cremated at a private ceremony.
Gee was openly homosexual.