Tiberius was born in 163 BC, son of Tiberius Sempronius Gracchus and Cornelia Africana. The Gracchii, though not of patrician stock, were one of the politically most important families of Rome, very rich and well connected. His mother was daughter of Scipio Africanus and his sister Sempronia was the wife of Scipio Aemilianus, another important general. Tiberius was raised by his mother, with his sister and his brother Gaius Gracchus.
Tiberius military career started in the Third Punic War, as military tribune appointed to the staff of his brother in law, Scipio Aemilianus. In 137 BC he was appointed quaestor to consul Gaius Hostilius Mancinus and served his term in Numantia (Hispania province). The campaign was not successful and Mancinius' army suffered a major defeat. It was Tiberius, as quaestor, that saved the army from destruction by signing a peace treaty with the enemy. Back in Rome, Scipio Aemilianus considered the attitude as cowardice and convinced the senate to nullify the treaty. This was the start of the political enmity between Tiberius and the senate.
Rome's internal political situation was not peaceful. In the last hundred years, there had been several wars. Since legionaries were required to serve in a complete campaign no matter how long it was, soldiers often left their farms in the hands of wives and children. As estates in this situation went steadily into bankruptcy and were bought up by the wealthy upper class, latifundi or large estates, were formed. When the soldiers returned from the legions, they had nowhere to go, so they went to Rome to join the mob of thousands of unemployed who roamed the city. Due to this, the number of men with enough assets to qualify to army duty was shrinking as the military power of Rome. In 133 BC Tiberius was elected tribune of the plebs. Soon he started to legislate on the matter of the homeless legionaries. Tiberius managed to approve a law called Lex Sempronia agraria saying that the government would buy the land possessed by the owners of latifundi in excess of 500 acres. This land would then be distributed to soldiers upon completion of their service. This would solve two problems: increase the number of men that could be levied for service and also taking care of homeless war veterans.
The senate and its conservative elements were strongly against the Sempronian agrarian reforms. They did not take much action against them, because there was not enough money currently to reimburse the landowners without disrupting other activities, and so Tiberius could have it approved but could not implement it. However, late in 133, king Attalus of Pergamon died and left his entire fortune to Rome. Tiberius saw his chance and immediately used his tribunician powers to allocate the fortune to fund the new law. This was a direct attack at senatorial power, since the house was traditionally responsible for the management of the treasury. His fellow tribune of the plebs, Gaius Octavius, tried to veto the law, but Tiberius had him removed illegally from his office. Senate opposition increased.
The year was at an end, as Tiberius' term as tribune. After that, there was no way he could protect his laws from being revoked. Tiberius decided to run for election to an unprecedented second term. The conservators of the senate were not pleased and soon the situation became violent. Tiberius was killed in 132 BC near the Capitol, during an armed confrontation with political enemies, lead by Publius Cornelius Scipio Corculum, his own cousin.
Tiberius was married to Claudia Pulcheria, daughter of Appius Claudius Pulcher (consul in 143 BC), and had three sons that died young. His main heir was his younger brother, Gaius Gracchus which, a decade later, would share his fate while trying to apply even more revolutionary legislation.
See also: Scipio-Paullus-Gracchus family tree
References
Plutarch, Life of Tiberius and Gaius Gracchus