Historic agreements have given Egypt and Sudan veto power over upstream projects that could affect the flow of water.
But the agreement signed last week by four of the Nile Basin countries marked the creation of a new commission to manage the water.
Kenya, Burundi and the Democratic Republic of Congo are expected to sign within a year.
Egypt has warned that the agreement lacks legitimacy.
But Zenawi told Al Jazeera's Andrew Simmons that Egypt's approach is out of date.
The source of the Nile, the longest river in the world, is Lake Victoria.
It is comprised of the White and Blue Niles. It stretches from the Kagera river in Burundi to the Mediterranean Sea in Egypt.
Shared by 10 countries - Burundi, Democratic Republic of Congo, Egypt, Eritrea, Ethiopia, Kenya, Rwanda, Sudan, Tanzania and Uganda - it runs 6,741km.
The overall population of these countries is over 300 million people. More than 160 million live along the Nile Basin.
"Some people in Egypt have old-fashioned ideas based on the assumption that the Nile water belongs to Egypt, and that Egypt has a right to decide who gets what, and that the upper [Nile basin] countries are unable to use the Nile water because they will be unstable and they will be poor," he said.
"These circumstances have changed and changed forever.
"Ethiopia is not unstable. Ethiopia is still poor, but it is able to cover the necessary resources to build whatever infrastructure and dams it wants on the Nile water."
The upstream countries want to be able to implement irrigation and hydro-power projects in consultation with Egypt and Sudan, but without Egypt being able to exercise the veto power it was given by a 1929 colonial-era treaty with Britain.
Legal action threatened
Egypt, however, has warned that Cairo's water rights are a "red line" and it threatened legal action if a unilateral deal was reached.
But Zenawi dismissed the warning, saying it would not solve the dispute at hand.
"The way forward is not for Egypt to try and stop the unstoppable. The way forward is to seek a win-win solution through diplomatic efforts," he said.
Al Jazeera's Amr El Kahky, reporting from Cairo, said Egyptian government officials said such statements undermine the spirit of co-operation between the Nile Basin Initiative countries.
"A government official told me that Egypt does not oppose the development of these countries," he said.
"But at the end of the day, Egypt does not want to see the flow of the Nile and the water share of the Nile being hindered or reduced."
Water supply fears
The new agreement, the Nile Basin Co-operative Framework, is to replace a 1959 accord between Egypt and Sudan that gave them control of more than 90 per cent of the water flow.
The two countries have expressed fears that their water supply would be severely reduced if the seven other Nile users divert the river with domestic irrigation and hydro-power projects.
The Nile Basin Initiative, which had been spearheading the talks, will now become the Nile Basin Commission and will receive, review and approve or reject projects related to Africa's longest river.
The commission will be based in Addis Ababa, Ethiopia's capital, and have representation from all nine Nile Basin countries.