In the first attack, a Palestinian drove into soldiers at a bus station near Kfar Adumim settlement, northeast of Jerusalem, and was shot dead, police said.
Police identified him as Fadi Hassib, from Ramallah, whose brother was shot dead on Sunday after ramming his car into Israelis before charging at them with a knife.
Israel's Magen David Adom emergency medical service said the two soldiers were taken to hospital in Jerusalem with light to moderate injuries.
Several hours later, another Palestinian was shot dead after driving his car into a group of soldiers, injuring five close to Beit Ummar settlement near Hebron in the southern West Bank, an army spokesman said.
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He identified the attacker as 20-year-old Omar Zaatik.
Today's incidents raise the number of Palestinians killed since October 1 to nearly 100, including an Israeli Arab.
Over half of them have been alleged perpetrators of stabbing, shooting and car ramming attacks aimed at Israeli civilians and security forces. Others have died in clashes with security forces.
Ten Palestinians and one Israeli soldier have been killed since the start of this week.
Today's incidents are the latest in a wave of unrest that has shaken Israel and the Palestinian territories since early October.
Each Friday, Palestinian movements headed by Islamist movement Hamas call for a "day of rage", which escalates into clashes between Palestinian youths throwing stones and Molotov cocktails and Israeli security forces who respond by shooting real or rubber-coated bullets and tear gas.
Today, clashes were reported across the occupied territories, wounding several people, according to the Red Cross which had yet to compile a full tally.
On Monday, Israeli Prime Minister Benjamin Netanyahu announced a series of new security measures likely to affect the daily lives of Palestinians in the West Bank.
He announced tighter controls on Palestinian vehicles and an increase in the number of so-called "bypass roads" which create separate routes for Palestinians and Jewish settlers.
During a visit to a West Bank settlement that has been the scene of numerous attacks, he also said work permits would be withdrawn from the families of alleged attackers.
Netanyahu added there would be "no limits" on the powers of Israeli soldiers in the West Bank, where some 400,000 Jewish settlers live among 2.8 million Palestinians.