Suzuki announced at a meeting of the prefectural assembly of Hokkaido.
The village of Tomari, which hosts the plant, and three nearby municipalities in Hokkaido have already expressed their approval.
The governor said that he will inform the Japanese government of his decision "at the earliest possible time."
Hokkaido Electric aims to restart the reactor as soon as possible in 2027.
The governor said that behind his approval was Hokkaido Electric's plan to lower its electricity rates following the restart, as well as his view that ensuring a stable power supply and decarbonising energy sources will lead to local economic growth.
"I agree with the restart," he said, noting that he also took into account the opinions of Hokkaido citizens and relevant municipal governments, as well as discussions at the Hokkaido assembly.
Regarding safety and disaster prevention measures at the Tomari plant, the governor said that he will urge the Japanese government and Hokkaido Electric to make all possible efforts, following a major earthquake that mainly struck the northeastern prefecture of Aomori, near Hokkaido, on Monday night.
The temblor measured up to upper 6, the second-highest level on the country's seismic intensity scale, in Aomori and up to upper 5, the fourth-highest level, in Hokkaido.
Later, he told reporters: "Deciding the pros and cons (of the restart) is the responsibility of a politician.
I have concluded that using nuclear energy is a realistic option that can be taken for the time being."
In the run-up to the envisaged restart, Hokkaido Electric plans to take fresh safety measures, such as constructing a new seawall.
Meanwhile, a lawsuit aimed at blocking the restart of the nuclear power plant is ongoing at the Sapporo High Court in Sapporo, the capital of Hokkaido.
After the Nuclear Regulation Authority concluded in July that the No. 3 reactor complies with new regulatory standards, the Japanese government asked the prefectural government of Hokkaido and the four municipalities, including the village of Tomari, in August to understand the restart.
Tomari and the three municipalities--the towns of Kyowa and Iwanai and the village of Kamoenai--have approved the restart.
Late last month, the governor indicated his support for the restart at a prefectural assembly meeting.
He visited the plant last Thursday to check safety measures there.
Suzuki has also met with the heads of the four municipalities, stating, "I will make a final decision based on the municipal leaders' decisions, which are serious."
[Copyright The Jiji Press, Ltd.]