The 54-year-old was killed instantly after being hurled from Westminster Bridge onto a stone walkway below after being hit by the rented Hyundai SUV driven by terrorist Khalid Masood.
Mr Cochran’s wife Melissa, 46, suffered a broken leg and rib as well as facial cuts as she remains in hospital following the deadly attack.
Clint Payne, Mr Cochran's brother-in-law, said: “Thank you for coming this morning, and most especially for your kindness and consideration of our family.
“This has been a humbling and difficult experience but we have felt the love of so many people during these past several days.
Kurt Cochran's family paid tribute following his death in the Westminster attack
“It’s been a tender experience for our family to be together with Melissa here. Her health is steadily improving and she has been strengthened by the presence of her family.
“She is so grateful for the outpouring of love and generosity.
“Our family is so grateful for the first responders, the medical personal, the assistance of government agencies and the United States and Great Britain.
“So many people have been so kind, and we are deeply touched by their goodness and their generosity.”
Kurt Cochran's family speaking at a press conference
Your notes, prayers, donations and love have helped us so much
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The couple from West Bountiful, Utah, had been in London celebrating their 25th wedding anniversary.
More than £50,000 has been collected for the family of Kurt Cochran and proceeds from the foundation will be used primarily to help Melissa with living expenses and loss of income.
The couple had visited Holland, Germany, Ireland and Scotland during their trip and were in London on their final day to spend time with Melissa's parents, who work as missionaries for the Church of the Latter Day Saints in the capital.
London mourns terror attack at vigil Fri, March 24, 2017
The world grieves after an attacker killed three people and injured about 40 near parliament in London.
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Floral tributes are left after the vigil in Trafalgar Square, London to remember those who lost their lives in the Westminster terrorist attack
Mr Payne added: “Your notes, prayers, donations and love have helped us so much. The most difficult part of all of this is that Kurt is no longer with us and we miss him terribly.
“He was an amazing individual, who loved everyone and tried to make the world a better place.
“He left a legacy of generosity and service that continues to inspire us. We are deeply saddened to lose him but are grateful that the world is coming to know him and to be inspired by him.
“Thank you for your many stories that have touched our family and helped us remember and celebrate his life.”