Local media report Mr Abe's ruling coalition has retained its two-thirds majority in parliament.
This paves the way for Mr Abe to amend Japan's post-war pacifist constitution.
The prime minister has previously called for the existence of the country's armed forces to be formalised, a controversial move which he says is needed to strengthen Japan's defence but which critics say is a step towards re-militarisation.
Speaking after the exit polls, Mr Abe said: "As I promised in the election, my imminent task is to firmly deal with North Korea.... For that, strong diplomacy is required."
The BBC's Rupert Wingfield-Hayes in Tokyo says Mr Abe's victory is partly thanks to Pyongyang's actions.
Just two months ago his popularity was plummeting as he was caught up in two messy political scandals, says our correspondent, but he enjoyed a sudden recovery after North Korea fired two missiles over the Japanese island of Hokkaido in recent months.
Local news outlets reported that Mr Abe's ruling Liberal Democratic Party (LDP) coalition with the Komeito party has won 312 of the 465 seats in the lower house of Japan's parliamentary Diet - which gives them the power to table a revision to the constitution.
Mr Abe had previously announced he wanted to revise a clause which renounces war, known as Article 9, to formally recognise Japan's military, which is known as the "self-defence forces".
He said he was ditching a previously-set deadline of 2020 to achieve the revision so that he would have more time to "gain support from as many people as possible" for the highly contentious task.
Even if an amendment to the constitution is passed and approved by both houses in the Diet - which Mr Abe's coalition controls - it still needs to be put to a public vote in a referendum.
Mr Abe two years ago successfully managed to push for a re-interpretation of the constitution to allow troops to fight overseas under certain circumstances, which attracted widespread protests.
But in the end it was overtaken by the centre-left Constitutional Democratic Party which emerged as the biggest opposition party, and which opposes Mr Abe's plan to amend Article 9.
Ms Koike, who was in Paris for a business trip during the election, told reporters she was personally taking responsibility for the result. Japanese media quoted her as saying her "words and deeds" had caused "displeasure" to voters.
A win in the election also raises Mr Abe's chances of securing a third three-year-term as leader of the LDP when the party votes next September.
That would give him the opportunity to become Japan's longest serving prime minister, having been elected in 2012.
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