Andreea Cristea is the fifth victim of the attack on 22 March, in which Khalid Masood drove into crowds on Westminster Bridge then stabbed a policeman to death, before being shot dead himself.
Ms Cristea, 31, who was on holiday with boyfriend Andrei Burnaz, had been in hospital since the attack.
It has emerged that Mr Burnaz had been planning to propose during the day out.
A family statement confirmed Ms Cristea, who was an architect, had died on Thursday.
The family said: "After fighting for her life for over two weeks, our beloved and irreplaceable Andreea - wonderful daughter, sister, partner, dedicated friend and the most unique and life loving person you can imagine - was cruelly and brutally ripped away from our lives in the most heartless and spiritless way.
"She will always be remembered as our shining ray of light that will forever keep on shining in our hearts."
The family said they were "deeply touched and eternally grateful" to the "never-ending dedication" of the medical staff who treated Ms Cristea, saying their "kindness and empathy are beyond compare".
"There are no words to even begin to describe the crushing pain and emptiness that is left in our hearts," they continued.