He is showing a dozen drawings which reveal his struggles with prison life, violence and mental health during 45 years in jail.
Bronson, who has changed his name to Charles Salvador, was chosen by curator Lisa Gray whose Flux exhibition showcases "the most talented, dynamic painters, sculptors and performance artists".
Ms Gray said: "I was instantly taken aback by the pureness of his work. Art that came straight from his soul.
"With such uninspiring surroundings, I found his talent very inspirational, often not easy to look at but bold, humorous and full of abstract and meaningful detail."
She said that as well as their shared passion for art, she and Salvador had common interests in helping young offenders and soldiers injured in combat.
"Many people think they know the myth that is Charles Bronson. Over the years his crimes have been exaggerated. He has served more time than murderers, the majority of which has been in segregation.
"Ninety-five per cent of crimes committed by Charles where inside the prison walls, some of which were provoked."
Salvador was originally jailed for armed robbery in 1974, but his time in prison has been extended many times by episodes of violence behind bars.
He has won prizes for his art, written several books and raised thousands of pounds for charity.
In the exhibition brochure, he writes: "I found art, I live for art, art is my life. I'm going to do my art and create masterpieces until my heart stops beating.
"I want to be one of the greatest artists. I am an artist, a man of peace. Art has saved me."
The exhibition at the National Army Museum in Chelsea, west London, opened on Thursday night with 1,000 VIP guests and runs until Sunday.
It also features the work of artist and musician Nick Reynolds, son of the Great Train Robbery mastermind Bruce Reynolds and a long-time friend of Charles Salvador.
One of his paintings depicts the transformation of Bronson to Salvador.
Mr Reynolds said: "Charlie and I go back a long way through his friendship with my dad and then through our mutual interest in art. His art deserves a wider audience."
Mr Reynolds is a member of the rock band Alabama 3 who played an acoustic set at the exhibition's opening.
He added: "Charlie's art at first glance may look comical and cartoonish but that only makes it all the more disturbing.
"Through his sense of dark humour he manages to visualise and convey his nightmarish world of incredible torment and suffering like a modern day Bosch.
"Despite the beatings and isolation he has miraculously managed to hang on to his sanity in what I believe is a true triumph of the spirit - a good artist is someone who can provoke an emotional response even better when they are able to transport you into their world, and Charles Salvador certainly does that.
"When I look at Charlie's work I'm overwhelmed by the tragedy that lies behind it all, I think of the figure in Munch's The Scream and marvel at Charlie's indefatigable sense of self."