TNT was formed in the Norwegian city Trondheim in 1982, by vocalist and rhythm guitarist Dag Ingebrigtsen, guitarist Ronni Le Tekrø, bassist Steinar Eikum and drummer Morten "Diesel" Dahl. Securing a national record contract with PolyGram subsidiary Vertigo Norway, they released their self-titled debut album the same year — their only album that features Norwegian lyrics — and got a hit with the single "Harley Davidson". In August 1983 Morty Black replaced Steinar Eikum on bass, and the following year American vocalist Tony Harnell became TNT's new frontman, making his debut on their album Knights of the New Thunder. His unique and powerful 4 octave range was the final element the band needed to break out of Norway and into the world market. The album was a huge success in Scandinavia and the band then was offered a worldwide deal with Mercury/Polygram worldwide out of New York. Knights was then released in the U.S. in 1985 and the video for Seven Seas got heavy rotation on MTV and the album entered the billboard charts.

That line-up recorded one more album, Tell No Tales in 1987, before "Diesel" Dahl was fired later that year after some turbulent times within the band. Tell No Tales produced TNT's biggest hit, the single "10,000 Lovers (In One)". Tell No Tales marked a slight change in sound from melodic Euro-metal to a more palatable hard rock style, with Le Tekrø and Harnell gaining a reputation as a talented duo. The album was the best selling release in Norway and Sweden that year (outselling hugely popular artists like Michael Jackson and Def Leppard). Tell No Tales also saw the band establishing a mainstream following in Japan and the U.S. Promotional Videos for "Everyone's a Star" and "10,000 Lovers (In One)" were featured on both European and American MTV. They were also featured on Headbangers Ball. The band supported Stryper on a sold out arena tour in the U.S. followed by a tour with Twisted Sister and Great White as well as headlining shows in large clubs in the U.S.

Kenneth Odiin became TNT's new drummer, but recorded only one album with the band, Intuition in 1989, before he left. This release marked a more AOR-oriented sound, still maintaining a little of the hard rock edge of the previous album. Intuition was another huge success in Scandinavia and Japan. It was also the band's best received American release and saw the band embarking on their first headlining tour of the U.S. which broke attendance records across the country in small theaters and large clubs, thanks to the prominent display of the video for the title track on MTV. After the touring to support the album was done, the band negotiated a new (and generous) record contract with Atlantic Records. With new drummer John Macaluso, TNT released the studio album Realized Fantasies and the live recording Three Nights in Tokyo (both in 1992). However, Atlantic did a poor job of promoting the album in the States (assuring that TNT would never find huge success in America) and also the rest of the world. The same year they decided to take a break, choosing to focus on various solo projects. In 1996 the compilation Till Next Time was released, and Harnell, Le Tekrø and Black reformed TNT with drummer Frode Lamøy. That line-up recorded two albums, Firefly in 1997 and Transistor in 1999.

"Diesel" Dahl returned to TNT in 2000, and the band started working on their new album My Religion, which was released in 2004. Months after the album release, Morty Black decided to quit, and Sid Ringsby took his place for the following concerts and the album All the Way to the Sun, which was released in the fall of 2005. A single, "Sometimes" was released on July 25 in Norway. At the end of that year Victor Borge became TNT's new permanent bassist.

Tony Harnell left the band in April 2006 for both personal and professional reasons, although his final show was on June 30, where TNT played the Polar Rock Festival in Storsteinnes, Norway. He was replaced by British hard rock singer Tony Mills (of UK act Shy, coincidentally supporting TNT for Harnell's farewell show). Despite leaving the band, Harnell collaborated with iMagic Films and producer Darren Paltrowitz on a live DVD featuring his performance with the band in Madrid, Spain from April 1, 2006. The Live in Madrid CD + DVD package was released in Japan in August 2006 and elsewhere in the world in September 2006.

In 2007 TNT released their tenth studio album, The New Territory to mixed reviews and controversy amongst the fans. No music videos to support the album were released.

TNT released its 11th studio album, Atlantis, on September 22, 2008 in both Norway and Japan. The album was influenced by The Beatles and Queen, and was mixed by Tommy Hansen, who also worked on My Religion and All the Way to the Sun.