Mr Suga, who is 71-years-old, played a key role in Mr Abe’s administration by acting as the government’s top spokesperson as chief cabinet secretary.
He is now expected to be elected as the new prime minister when a parliamentary vote is held later this week.
Victory in the vote to lead the ruling Liberal Democratic Party all but guarantees Mr Suga will be elected as PM on Wednesday due to the majority held by the party’s ruling coalition.
“Now I'm handing the baton to new LDP President Suga,” Mr Abe said after the vote.
“We can count on him.”
Mr Suga received 377 votes in Monday’s election to succeed Mr Abe, while former foreign minister Fumio Kishida received 89 votes and former defence minister Shigeru Ishiba received 68.
The new leader, who has been a loyal supporter of Mr Abe, said his main priorities would be fighting the coronavirus pandemic and turning around Japan’s battered economy.
“I will devote all of myself to work for the nation and the people,” he said in his victory speech.
Mr Suga’s victory was ensured by gaining the support of party heavyweights early in the campaign on the expectation that he would continue the policies of Mr Abe, who resigned abruptly last month due to chronic illness.
During his time in politics, Mr Suga has repeatedly praised Mr Abe’s diplomacy and economic policies, while also defending the government over scandals related to alleged favouritism and cronyism.
In addition to the coronavirus pandemic, the new LDP leader will be tasked with navigating Japan’s strained relationship with China, deciding what to do with the postponed Tokyo Olympics and establishing a good relationship with whoever wins the US presidential race.
Although he could be a caretaker prime minister until the end of Mr Abe’s scheduled term in September 2021, some analysts have suggested he could stay in power longer.
“I think he has a more holistic view of politics and the government than maybe a lot of people who have occupied the post of prime minister,” Tobias Harris, a political analyst, told AP.
Mr Harris added that Mr Suga, who grew up in rural Japan and is not tied to one faction in the LDP, could prove to be a political realist with a broader national perspective than Mr Abe.
Wang Wenbin, China’s foreign ministry spokesperson, congratulated Mr Suga on Monday and expressed willingness “to deepen cooperation in the fight against the epidemic and economic and social development, and continuously promote improvement and development of China-Japan relations.”
Additional reporting by AP