Two University of Cambridge graduates, Jack Merritt, 25, and Saskia Jones, 23 were killed Friday, and three others were injured.
Khan, 28, who was wearing a fake suicide vest, was confronted by civilians before he was shot and killed by police.
His family expressed condolences to the victims and condemned his actions in a short statement released through the Metropolitan Police.
"We are saddened and shocked by what Usman has done," the statement read. "We totally condemn his actions and we wish to express our condolences to the families of the victims that have died and wish a speedy recovery to all of the injured."
The family also requested privacy "at this difficult time."
Khan was released from prison in 2018 after he was convicted for planning terror attacks, including one targeting at the London Stock Exchange in 2010.
Merritt's girlfriend, Leanne O'Brien, also released a statement Monday, describing her boyfriend as a "phenomenal man."
"My love, you are phenomenal and have opened so many doors for those that society turned their backs on," she wrote on Facebook.
Merritt and Jones were attending prisoner rehabilitation event they were supporting at London's Fishmongers' Hall at the time of the attack.
Dozens of people gathered in central London Monday for a vigil honoring the victims.