Micky Rosenfeld, spokesman for the police, said: "He admitted to carrying out the terrorist attack."
Several other Palestinians have also been arrested in connection with the attack.
The blast was the first bombing in Israel's business capital in six years, the last such attack taking place during Passover 2006, when a suicide bomber at a café killed 11 people.
It was the first bus bombing in Tel Aviv in more than 10 years.