"A convoy of 80 trucks transporting humanitarian aid has started to pass through the Kerem Shalom crossing" in the south, a military spokesman said.
The aid included medicine and food which was sent from Egypt, Jordan, Greece and UN aid agencies, he said.
The Nahal Oz terminal in the north was also opened on Monday to allow the transfer of 200,000 litres of fuel for Gaza's electricity station as well as 120 tonnes of cooking gas, he said.
The Erez crossing in the north meantime was opened to allow some 200 Palestinian holders of foreign passports to leave the territory.
Israel unleashed a massive bombing campaign of Hamas targets in Gaza on December 27 in response to consistent rocket fire from the territory and poured in ground troops to back up the bombardments a week later.
Aid groups have repeatedly warned of a worsening humanitarian crisis in the densely-populated territory, where most of the 1.5 million residents depend on foreign aid.