They said their 20-year-old daughter had been taking part in an archaeological dig the morning she was killed.
Ms Bladon, a University of Birmingham student, had been on an exchange programme with the Hebrew University of Jerusalem since January.
She was stabbed several times in the chest while travelling on a tram near the Old City and died shortly after the attack in hospital.
In a statement issued throughout the Foreign and Commonwealth Office, Ms Bladon’s family said: “Hannah was the most caring, sensitive and compassionate daughter you could ever wish for.
“Hannah was a talented musician, part of a serving team at her local church and a member of her local archaeological group,” the statement continued.
“She was an enthusiastic rugby player and a keen Derby County supporter.
“She was driven and passionate and her death leaves so much promise unfulfilled.
“Our family is devastated by this senseless and tragic attack.”
Witnesses say they saw Ms Bladon’s attacker pull a knife out of his bag and stag Ms Bladon several times in the upper part of her body as the tram was approaching City Hall.
An off-duty policeman who was on the tram with his family pulled the emergency brake and charged at the Palestinian man.
A 30-year-old pregnant woman and a 50-year-old man were also injured in the attack.
A 57-year-old man was arrested at the scene. Police believe he suffers from mental illness.
The University of Birmingham released a statement saying it was “deeply saddened” over Ms Bladon’s death.
It said it would be offering support to any students affected.
The Hebrew University of Jerusalem also expressed “deep sorrow” over the loss.
The school said in a statement: “We extend our deepest condolences to her family and we share in their sorrow.
“The university condemns such acts of terror that harm innocent people, and especially a student who came to Jerusalem to study and widen her academic horizons.”
The university department that Ms Bladon studied with said she was taking Bible studies, archaeology and Hebrew courses during her exchange programme.
The Rothberg International School said Ms Bladon’s “friends described her as an inquisitive and adventurous student who made the most of her opportunity to learn and experience life in Israel”.
Israel President Reuven Rivlin said he was “filled with sadness” over the attack and that his country’s “thoughts and prayers are with the family of the victim”.
He said: “This week thousands have come through the ancient gates of Jerusalem to celebrate the feasts of Passover and Easter throughout the city – while the security forces work to ensure the safety of the dear residents and visitors to the city.
“And so we will continue to do. Terror can never overcome us. Terror will never destroy our lives here.”
Jerusalem has been on high alert during Holy Week after an increase in knife attacks by Palestinians.
Palestinians have killed 42 Israelis and two visiting Americans, mainly in stabbings, car ramming assaults and shooting attacks since September 2015.
Israeli forces have killed at least 243 Palestinians during that time, most of them identified as attackers by Israeli authorities.