Mr Suga, 71, was chosen as the new head of Japan's ruling party, receiving 377 votes in an election to pick a successor.
Shinzo Abe announced last month that he would resign due to health problems.
Mr Suga's victory all but guarantees his election in a parliamentary vote on Wednesday because of the majority held by the Liberal Democrats' ruling coalition.
He is a close ally of Mr Abe and currently the chief cabinet secretary in the administration.
Mr Suga, the son of a farmer in northern Japan's Akita prefecture, said he had come a long way.
"I will devote all of myself to work for the nation and the people," he said in his victory speech.
"Now I'm handing the baton to new party leader Suga," Mr Abe said after the vote. "We can count on him."
Mr Suga said his top priorities are fighting the coronavirus and turning around a Japanese economy battered by the pandemic.
Shinzo Abe stepped down in August.
The 65-year-old is suffering with ulcerative colitis - a long-term condition where the bowel becomes inflamed - and was hospitalised twice in a week.
His term as PM was due to end in September 2021. He called the decision to resign "gut-wrenching".
Mr Suga gained the support of party heavyweights early in the campaign on expectations that he would continue Mr Abe's policies.
The other two contenders in the election received a combined 157 votes.
Former foreign minister Fumio Kishida received 89 votes, while former defence minister Shigeru Ishiba got 68.
Despite his low-key image as Mr Abe's right-hand man, Mr Suga is known for his iron-fist approach to getting jobs done as a policy coordinator and influencing bureaucrats by using the centralised power of the prime minister's office.
Mr Suga says he is a reformist and that he has worked to achieve policies by breaking territorial barriers of bureaucracy.
He has credited himself for those efforts in achieving a booming foreign tourism industry in Japan, lowering mobile phone bills and bolstering agricultural exports.
In addition to the coronavirus and the economic fallout, Mr Suga stands to inherit several other challenges, including China, which continues its assertive actions in the East China Sea.
He also will have to decide what to do with the Tokyo Olympics, which were pushed back to next summer due to the coronavirus.
And he will have to establish a good relationship with whoever wins the US presidential race.