Hundreds of Venezuelans have been crossing into Colombia to buy products that are scarce in their country.
President Maduro had closed the border at the same time as announcing the withdrawal of the country's highest denomination bank note.
He has accused criminal gangs of hoarding vast amounts of cash.
Products subsidised by Venezuela's socialist government, including petrol, sugar and flour, can also end up being sold on the Colombian side of the border at much higher prices.
President Maduro and his Colombian counterpart, Juan Manuel Santos, agreed to the gradual reopening in a phone call on Monday.
Up to 2,000 people are expected to cross from Venezuela into Colombia on the first day, according to Colombian RCN radio.
"When I heard the news, I decided to come to the border crossing very early," Carolina Correa told RCN in the Venezuelan border city of Cucuta.
"I need rice, sugar, a new pot and other ingredients for the Christmas meal, as well as medication for my mother," she added.
Mr Maduro had argued the withdrawal of the 100-bolivar bill was vital to tackle "mafias" attempting to destroy the country.
But the measure sparked chaos, with protests and long queues forming outside bank branches.
The government was eventually forced to postpone the deadline for exchanging the notes until 2 January.
Venezuela is facing a major economic crisis, which the opposition blames on the mistaken policies of its socialist government.
Venezuela has reopened its border with Colombia, eight days after President Nicolas Maduro closed it in order to combat smuggling.