This was announced in a joint statement following a meeting at the state palace in Bogor, outside Jakarta, between Indonesian President Joko Widodo and Malaysian Prime Minister Ismail Sabri Yaakob.
Mr Widodo, better known as Jokowi, said he had a "very open and friendly" discussion with his Malaysian counterpart on several topics, including protection for migrant workers, land and sea borders, as well as regional issues such as Myanmar and the South China Sea.
"As close neighbours and peoples of a common race, we must strengthen our cooperation based on the principle of mutual respect and mutual benefit," said the Indonesian leader.
"We have agreed to make a travel corridor arrangement in stages, that we will launch one by one," he added.
Datuk Seri Ismail said the two leaders agreed to implement a vaccinated travel lane.
He added that the relevant ministers will study the travel matter in detail, although he raised the possibility that the lanes between Kuala Lumpur and Jakarta, as well as the resort island of Bali, could be opened first.
"In the early stage, we may start with KL-Jakarta-KL and KL-Bali-KL," he said.
"God willing, we will expedite with the details and make a joint statement to announce the reopening of the borders," he added.
Accompanied by several ministers, the Malaysian Prime Minister's visit to Jakarta is his first since he was sworn into office on Aug 21.
Mr Ismail, who arrived on Tuesday and will be in the Indonesian capital until Thursday, was given a 19-gun salute at the official welcoming ceremony at the palace on Wednesday. Mr Widodo also hosted a state banquet for Mr Ismail.
State visits by new leaders in both countries are a diplomatic tradition.
Mr Widodo visited Kuala Lumpur in 2015, and, in turn, received former Malaysian premiers, Tun Dr Mahathir Mohamad, in June 2018 and Tan Sri Muhyiddin Yassin in February this year.
Malaysia's Foreign Ministry said in a statement on Tuesday: "The visit will open a new chapter in the already strong, multifaceted Malaysia-Indonesia relations. It will provide an opportunity for the leaders to advance collaboration towards effective recovery as two immediate neighbours deal with the impacts of the unprecedented Covid-19 pandemic."
The two leaders on Wednesday witnessed the signing of two memoranda of understanding (MOU) on education and Customs by their ministers.
Before leaving Jakarta, Mr Ismail is scheduled to meet Indonesian businessmen, the chief editors of Indonesian media and Malaysian residents in Indonesia.
He is also due to visit a defence industry facility in Bandung, West Java.