The man, 54, is believed to have been killed while walking on Westminster Bridge as a car mowed down pedestrians.
He and his wife, Melissa, were believed to be two of the first people mown down by the vehicle. He died of his injuries.
Mr Cochran is believed to have either jumped or been pushed over the edge of the bridge onto steps beneath it.
Mrs Cochran, 46, was also injured in the attack.
She sustained a broken leg and rib and a head injury, but it is not believed to be critical.
Mrs Cochran's sister, Shantell Payne, wrote on Facebook: "With a heavy heart I must pass the sad news of our beautiful brother, father, husband, son and friend Kurt Cochran.
Kurt was a keen musician Credit: Facebook
"He could not overcome the injuries he received in the London terror attacks.
"This pain is so heart wrenching and raw it has rocked our family and all that knew him to its core.
"We will miss Kurt beyond words.
"We love you Kurt. RIP.
"Melissa Payne Cochran is in the hospital with a broken leg, rib and a cut on her head but will recover from her injuries. Sending all the love to her for a quick recovery."
Mr Cochran appeared to have been travelling around Europe this month, having posted photographs of his recent visit to Holland, Germany, Scotland and Ireland on his Facebook page.
He and his wife were reportedly due to return home next week.
He was a keen musician, according to friends who posted their condolences on social media, and he played the guitar from the age of seven.
Melissa, his wife, is believed to be in hospital Credit: Facebook
Mr Cochran described himself as a "self-starting business owner" and spoke frequently of his passion for music.
In a 2014 interview with a local newspaper about his business, he spoke about his background.
He said that he "grew up in Maryland, lived in Texas for a while, then ended up in Salt Lake City in 1983."
Mr Cochran was also a big rock music fan, explaining: "As I grew older, hard rock/heavy metal took over as my favorite genres, like Black Sabbath, Judas Priest, Rush and Aerosmith."
He also spoke of how his parents got him interested in music, telling the paper: "My parents were big into music and entertaining. Mom loved jazz and Dad loved country. Music was very prevalent in my early years.
"I have a sister who is 10 years older than I am, and I used to sneak into her room and listen to Hendrix, Cream and Crosby, Stills, Nash & Young".
The musician also played in a band with his friend. He explained: "One day, my best friend was goofing around on a Casio keyboard and I picked up my guitar, and we started jamming. At that moment, we started a band. We played for a few years, played a few gigs and then decided that instead of a half-assed band we would build a kick-ass studio.
"So we did. We kicked around many names and because the studio is located on historic Onion Street in West Bountiful, the name Onion Street Studio became the obvious choice."
The music fan managed to achieve his dream of opening his own recording studio in 2007, and it appeared to be a roaring success, with customers giving it rave reviews.
One customer wrote: "I cannot say enough good things about Onion Street Studio. Very reasonable pricing. Creative and productive environment. Flexible hours and great people. I never felt pushed or pigeonholed into a direction I did not want to go. I will never use anyone but OSS! All around great experience!"
/The Telegraph/
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