Last month Mr Abe announced his resignation due to health reasons.
Mr Suga, 71, serves as chief cabinet secretary in the current administration and was widely expected to win.
He is considered a close ally of Mr Abe and likely to continue his predecessor's policies.
As had been widely expected, Mr Suga won by a large margin, taking 377 of a total of 534 votes from his party's lawmakers and regional representatives.
Now that the conservative Liberal Democratic Party (LDP) has chosen its new leader, there will be another vote on Wednesday in parliament, where he is almost certain to be made prime minister because of the LDP's majority.
Taking over mid-term, Mr Suga is expected to finish the rest of the current period, until elections in September 2021.