But he said Greeks faced a difficult road and recovery from financial crisis would only come through hard work.
Syriza has won just over 35%, slightly down on its previous result.
That is again short of a majority, but Syriza will form a coalition with the nationalist Independent Greeks. Conservative New Democracy won 28%.
The far-right Golden Dawn, which is set to be the third biggest party, won 7% of the vote compared with 6.3% in the election in January when Mr Tsipras was first elected.
Sunday's snap election was called after Syriza lost its majority in August.
Some of his MP's defected in protest at the signing of an unpopular new financial bailout deal with international creditors and formed the Popular Unity party.
But the new party has failed to gain enough votes to enter parliament.
Turnout in Sunday's poll was low by Greek standards at just over 55%.
"I feel vindicated because the Greek people have a clear mandate to carry on fighting inside and outside our country to uphold the pride of our people," Mr Tsipras told supporters in Athens.
"In Europe today, Greece and the Greek people are synonymous with resistance and dignity, and this struggle will be continued together for another four years."
Mr Tsipras was joined on stage by Panos Kammenos, leader of the the nationalist Independent Greeks, who also entered a coalition with Syriza after January's election.
"Together we will continue the struggle we began seven months ago," Mr Tsipras said.
Greece remains recession and the new government has to satisfy international creditors that it is fulfilling the terms of the latest bailout package worth up to €86bn ($97bn, £61bn).
Creditors are due to review the progress of the programme in October. Some Syriza MP's remain opposed to its terms.
Jeroen Dijsselbloem, who heads the Eurogroup meetings of eurozone finance ministers, said he was "ready to work closely" with the new Greek government.
The Greek electoral system means the party with the largest number of votes wins a bonus of 50 seats - and Syriza is predicted to have 145 seats in the 300-seat parliament, only four fewer than in Mr Tsipras's January victory.
The Independent Greeks, which is anti-austerity but agrees with Syriza on little else, won 10 seats. New Democracy won 75.
Mr Tsipras's popularity had to appeared to suffer after signing the bailout deal.
A referendum called by him saw 60% of voters reject the austerity measures demanded by creditors.